Condensed Matter Physics contains original and review articles in the field of statistical mechanics and thermodynamics of equilibrium and nonequilibrium processes, relativistic mechanics of interacting particle systems.The main attention is paid to physics of solid, liquid and amorphous systems, phase equilibria and phase transitions, thermal, structural, electric, magnetic and optical properties of condensed matter. Condensed Matter Physics is a diamond open-access, international peer-reviewed scientific journal published quarterly. ISSN 1607-324X (print), 2224-9079 (online) Key title: Condensed Matter Physics Abbreviated key title: Condens. Matter Phys.
Yukhnovskii Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine
The influence of dimensional crossover on phase transitions and critical phenomena in condensed systems
This article is aimed at studying the effects of the dimensional crossover (DC) on physical properties of condensed systems near phase transition and critical points. Here we consider the following problems: (1) the theoretical provisions that allow to study the effect of spatial confinement on DC near phase transition and critical points; (2) the study of DC in condensed systems with the Ginzburg number Gi < 1, where fluctuation effects are described in different ways at the fluctuation, regular and intermediate (crossover) regions; (3) two types of DC were investigated: (a) a decrease in the linear dimensions L to the values of the correlation length of the order parameter fluctuations leads to the conversion of the dependence on thermodynamic variable into a dependence on linear sizes of 3D systems, as well as (b) a further decrease in linear sizes L the 3D–2D or 3D1D DC happens depending on slitlike or cylindrical geometry, which is determined by the value of the lower crossover dimensionality dLCD; (4) it is proposed to extend the known equalities for critical exponents by using the Mandelbrot formula for fractal dimension Df as a critical exponent; (5) the influence of 3D–2D DC on the characteristics of the fine structure of the molecular light scattering (MLS) spectrum is studied.
Сollection of the articles dedicated to the 100th anniversary of Prof. Ihor Yukhnovskii
Copyright (c) 2025 O. V. Chalyi, E. V. Zaitseva https://creativecommons.org/licenses/by/4.0
Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton SEIRS model with temporal immunity and vaccination
We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is possible by restricting the transmission rate, increasing identification and isolation rate of infected individuals, and via vaccination. For the compartmental version of this model, we found stable diseasefree and endemic stationary states. The basic reproductive number is analysed with respect to balancing quarantine and vaccination measures. The positions and heights of the first peak of outbreak are obtained numerically and fitted to simple in usage algebraic forms. Lattice-based realization of this model is studied by means of the asynchronous cellular automaton algorithm. This permitted to study the effect of social distancing by varying the neighbourhood size of the model. The attempt is made to match the quarantine and vaccination effects.
Special issue dedicated to the 75th anniversary of Prof. Stefan Sokołowski
Copyright (c) 2026 J. Ilnytskyi, T. Patsahan https://creativecommons.org/licenses/by/4.0
How does ethane wet different substrates?
Computer simulations are employed to investigate the adsorption mechanisms of ethane on both homogeneous and inhomogeneous substrates. For homogeneous surfaces, the full range of surface phase transitions—from incomplete to complete wetting — can be accessed by tuning the strength of the surface potential. The resulting layering transition temperatures show excellent agreement with experimental measurements of ethane on graphite. By contrast, although all inhomogeneous substrates exhibit a prewetting transition, the adsorption mechanisms are strongly influenced by the stripe width.
Copyright (c) 2026 Ł. Baran, D. Tarasewicz, W. Rżysko https://creativecommons.org/licenses/by/4.0
Pressure effects in the properties of simple monohydric alcohols. Lessons from molecular dynamics simulations of united atom type UAM-EW model
We explore the pressure dependence of a set of properties of simple monohydric alcohols, namely of methanol, ethanol and 1-propanol, by using isobaric-isothermal molecular dynamics computer simulations. A recently proposed united atom, non-polarizable force field for each of alcohols [V. García-Melgarejo et al., J. Mol. Liq., 323, 114576 (2021)] is applied. Accuracy of the force field is evaluated by comparing the simulation results and available experimental data from the literature. Specifically, the density of alcohols upon increasing pressure, the isothermal compressibility, the static dielectric constant and self-diffusion coefficient are investigated starting from 1 bar up to 3 kbar. Evolution of the microscopic structure under pressure is discussed in terms of the pair distribution functions and some coordination numbers. Conclusions of the present modelling and necessary developments to consider in future work are commented on.
Copyright (c) 2026 M. Aguilar, L. Pusztai, O. Pizio https://creativecommons.org/licenses/by/4.0
Surfactant solutions confined in homogeneous and Janus-like slits
We study the behavior of aqueous surfactant solutions in the bulk phase and in slit-like pores by molecular dynamics. Adsorption and self-assembly of nonionic surfactants C7E3 that mimic alkyl poly(ethylene oxide) molecules are investigated. We consider pores with the same walls and Janus-like slits. The individual walls are inert, hydrophilic, or hydrophobic. We focus on the morphology of the surfactant solution confined in different slits. The influence of a pore type and its width is discussed. The aggregative adsorption of surfactants was found. Our simulations show that in slits surfactants assemble into structures that do not occur in the bulk phases.
Copyright (c) 2026 T. Staszewski, M. Borówko https://creativecommons.org/licenses/by/4.0
Molecular dynamics study of perchloric acid using the extended Madrid-2019 force field
Perchloric acid (HClO4) is widely used to prepare perchlorate salts with applications in propellants, industry, environmental chemistry, and biology. In this work, we used the intermolecular parameters from the extended Madrid-2019 force field for the perchlorate anion (ClO4-) and the oxonium cation (H3O+) together with TIP4P/2005 water to model perchloric acid solutions. The force field uses scaled charges of ±0.85e for monovalent ions and has been widely applied for aqueous ionic systems. We used the model to predict thermodynamic properties [densities and temperatures of maximum in density (TMD)], structural features (ion-water correlations: ion-hydrogen and ion-oxygen), and transport properties (self-diffusion coefficients and viscosity) of perchloric acid solutions at several concentrations. Experimental densities are predicted in excellent agreement up to 10 m. We also performed molecular simulations over a wide range of temperatures in order to determine the TMD of perchloric acid at different mol lities. Predicted viscosities at 298.15 K and 1 bar are in good agreement with experimental data for concentrations below 4 m. Results are discussed in terms of model strengths and limitations.
Copyright (c) 2026 M. Cruz-Sánchez, S. Blazquez, C. Vega, V. M. Trejos https://creativecommons.org/licenses/by/4.0
Symmetric mixtures in slit-like pores with selective walls
Symmetric mixtures characterized by high negative geometric and energetic non-additivity do not exhibit phase separation in the bulk. However, the phase separation occurs when such mixtures are confined in slit pores with selective walls. It is demonstrated that the wall selectivity affects the pore filling. When the difference of the interaction energies between the mixture components and pore walls is lower than a certain threshold value, condensation occurs between a dilute phase and the mixed liquid. When this difference exceeds the threshold value, the pore filling may occur in two steps. The first is the condensation of a dilute phase into the demixed liquid, and the second step leads to the formation of the mixed liquid. We have elucidated the changes in the phase behavior caused by non-additivity of symmetric mixtures, and by the difference in the interaction energies of the components with pore walls.
Copyright (c) 2026 A. Patrykiejew https://creativecommons.org/licenses/by/4.0
The application of Kirkwood-Buff theory to study hydration properties of α-amino acids
Protein conformational stability and function depend on non-covalent interactions that are strongly influenced by the surrounding environment. To explore protein properties, amino acids are often utilized as model systems. In this study, we determined the densities of seven α-amino acids in aqueous solutions between 278.15 K and 308.15 K and calculated the apparent molar volumes. Linear extrapolation yielded standard molar volumes, which were analyzed to characterize amino-acid hydration. The contributions of side chains to the standard molar volume were determined relative to glycine. The standard molar volume increased with temperature, indicating reduced electrostriction of water around the amino acids, consistent with lower hydration numbers at higher temperatures. We employed the Ornstein-Zernike integral equation with hypernetted-chain closure and a coarse-grained Lennard-Jones bead model to calculate pair correlation functions and Kirkwood-Buff integrals, from which standard molar volumes were obtain. The model reproduced the experimental standard molar volumes very well.
Copyright (c) 2026 Z. Štefanič, B. Hribar-Lee https://creativecommons.org/licenses/by/4.0
Multiscale theory, modelling, and simulation of hemicellulose and lignin in solution
This review examines multiscale modelling approaches for cellulose nanocrystals (CNCs) and lignocellulosic plant cell walls, with a focus on hemicellulose and lignin interactions in aqueous environments. The threedimensional reference interaction site model with the Kovalenko–Hirata closure (3D-RISM-KH) is highlighted as a powerful molecular solvation theory applied in nanochemistry and biomolecular simulations. The method has been successfully employed to investigate hemicellulose hydrogels, the influence of hemicellulose composition on nanoscale forces in primary cell walls, and lignin-lignin and lignin-hemicellulose interactions. Findings indicate that these interactions are predominantly hydrophobic and entropy-driven, arising from water exclusion effects. Insights gained through this modeling framework deepen the understanding of molecular-scale forces in plant cell walls and inform strategies for biomass valorization, including genetic engineering and pretreatment technologies aimed at enhancing cellulose extraction and utilization.
Copyright (c) 2026 A. Kovalenko https://creativecommons.org/licenses/by/4.0
Vortex formation in the Vicsek model with internal chirality of self-propelling objects
Effect of internal chirality on collective motion of a large number of active objects is studied by simulations of appropriately modified Vicsek model. We add a fixed angle to the noise and consider small ratios, p, between this angle and the maximal deviation from the average local direction of motion. When the above ratio is p = 1/120, the traveling bands observed with the symmetrical noise are destroyed, and small bands moving in different directions appear. Circular rotating flocks of objects with the same orientation are formed for p = 1/7.5. Stable vortexes in the stationary state were found from p = 1/60 to p = 1/20. Velocity autocorrelation function shows equilibrium between the inflow and the outflow to and from the vortex. Long-time evolution is considerably influenced by a temporary trapping of the objects in the vortex. The ballistic behavior for the symmetrical noise changes to the diffusive behavior for the chirality leading to the onset of vortexes.
Copyright (c) 2026 A. Ciach, W. Gozdz https://creativecommons.org/licenses/by/4.0
II. Temperature trends in the properties of simple monohydric alcohols. Molecular dynamics simulations of united atom UAMI-EW model
We explore the dependence of a wide set of properties of monohydric alcohols on temperature by using the isobaric-isothermal molecular dynamics computer simulations. Namely, methanol (MeOH), ethanol (EtOH) and 1-propanol (PrOH) alcohols are studied. The recently proposed united atom, non-polarizable force field for each of alcohols [V. García-Melgarejo et al., J. Mol. Liq., 2021, 323, 114576] is applied for this purpose. Accuracy of the force field is discussed comparing predictions from simulations and experimental data for density, dielectric constant, surface tension, and self-diffusion coefficient. Supplementary insights concerning applicability of the model are obtained by exploration of the composition dependence of various properties for MeOH–PrOH mixtures. Peculiarities of mixing of species in this system are elucidated in terms of density, excess mixing volume and excess mixing enthalpy. Static dielectric constant of the mixture and the corresponding excess are obtained. Perspectives of modelling are commented finally.
Copyright (c) 2026 M. Aguilar, E. Núñez-Rojas, O. Pizio https://creativecommons.org/licenses/by/4.0
Thermodynamics of hard-sphere fluids in polydisperse random porous media: Extended scaled particle theory
Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a hard-sphere (HS) fluid confined in size-polydisperse HS random porous media, extending the existing approaches to higher matrix packing fractions. We calculate chemical potentials for a wide range of porousmatrix parameters, including the matrix packing fraction, degree of polydispersity, and particle-size distributions. Within the proposed framework, our results show excellent agreement with available Monte Carlo simulations and previous integral-equation theories over a broad range of matrix packing fractions, 0.1 ≤ η0 ≤ 0.3, and degrees of polydispersity.
Copyright (c) 2026 T. Hvozd, M. Hvozd, M. Holovko https://creativecommons.org/licenses/by/4.0
Behaviour of the model antibody fluid constrained by rigid spherical obstacles: effects of the obstacle-antibody binding
We study a simplified model of monoclonal antibodies confined in a patchy random porous medium. Antibodies are represented as Y-shaped particles composed of seven tangential hard spheres with attractive patches on the terminal beads, while the matrix consists of randomly distributed hard-sphere obstacles bearing adhesive sites. The model captures antibody behavior in crowded biological environments with strong short-range antibodymatrix attractions. The theoretical approach combines Wertheim’s multidensity thermodynamic perturbation theory, the Flory-Stockmayer theory of polymerization, and scaled particle theory for fluids in porous media. We analyze thermodynamic properties, percolation thresholds, and phase behavior, and compare the selected results with new computer simulations. The interplay between antibody-antibody and antibody-matrix interactions produces a complex phase behavior, including re-entrant phase separation with a closed-loop coexistence region at higher temperatures and conventional liqui-gas separation at lower temperatures.
Copyright (c) 2026 Yu. Kalyuzhnyi, T. Patsahan https://creativecommons.org/licenses/by/4.0
Advances in the microscopic theory of inhomogeneous fluids: A tribute to Stefan Sokołowski on his 75th Birthday
This special issue is a collection of papers written by friends and colleagues of Prof. Stefan Sokołowski in memory of 75 years from his birth. We remember and miss him. This foreward contains a brief description of scientific contributions by Stefan principally focused in the construction of microscopic theory of inhomogeneous fluids. It refers mostly to our happy times while working together alog some of the topics mentioned below.We apologize that several issues of scientific interest have not been discussed in detail. Nevertheless, we hope that this text reflects motto of Stefan’s personality and besides will attract the attention of younger readers to a set of problems unsolved so far.
Copyright (c) 2026 J. Ilnytskyi, T. Patsahan, O. Pizio https://creativecommons.org/licenses/by/4.0
Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
The 70th Birthday of DSc Oksana Patsahan
On the 70th anniversary of Professor Tony Haymet
Investigation of density of states and charge carrier mobility in amorphous semiconductors via time-of-flight photocurrent analysis
The present study examines the electronic transport characteristics of amorphous semiconductors through ToF measurements and numerical simulations. The primary objective is to determine the DOS in amorphous selenium (a-Se) and to assess the temperature and electric field dependence of the hole mobility. A comprehensive investigation of localized states within the mobility gap is performed using Laplace transform analysis of ToF photocurrent transients, combined with the multiple trapping model. This approach enables accurate reconstruction of the DOS across a wide temperature range, allowing clear identification of shallow and deep trap levels and revealing thermally activated transport mechanisms. Simulated ToF currents are also used to evaluate the hole drift mobility under various thermal and field conditions. Activation energies are extracted from Arrhenius plots of the mobility data. The results support a physically consistent description of the electronic structure in a-Se and validate the applicability of Laplace-based techniques for probing charge transport in disordered semiconductors.
Copyright (c) 2025 F. Serdouk, A. Boumali, M. L. Benkhedir, Y. Goutal https://creativecommons.org/licenses/by/4.0
First principle study of electronic, magnetic and thermoelectric properties of Co2YPb (Y = Tc, Ti, Zr and Hf) full Heusler: Application to embedded automotive systems
In this study, theoretical investigation on structural, electronic, magnetic, elastic and thermoelectric properties of the full Heusler Co2YPb (Y = Tc, Ti, Zr and Hf) alloys have been performed within density functional theory (DFT). The exchange and correlation potential is addressed using two approximations: the generalized gradient approximation (GGA) and the GGA augmented by the Tran–Blaha-modified Becke–Johnson (mBj-GGA) approximation, which provides a more accurate description of the energy band gap. The electronic and magnetic properties reveal that the full-Heusler alloys Co2YPb (with Y = Tc, Ti, Zr, and Hf) display half-metallic ferromagnetic behavior. Furthermore, the elastic properties suggest that Co2YPb are mechanically stable, with ductile characteristics. p-type full Heusler alloys exhibit positive Seebeck coefficients and high ZT values, indicating good thermoelectric performance in terms of electrical and thermal conductivity. This leads us to the conclusions that these compounds are very interesting in improving the performance of embedded automotive systems and can also be used in spintronic devices.
Copyright (c) 2025 N. Saidi, A. Abbad, W. Benstaali, K. Bahnes https://creativecommons.org/licenses/by/4.0
Be and Be-related impurities in diamond: density functional theory study
First-principles density functional simulations were employed to investigate the geometries, electrical properties, and hyperfine structures of various beryllium-doped diamond configurations, including interstitial (Bei), substitutional (Bes), and beryllium-nitrogen (Be-N) complexes. The incorporation of Be into the diamond lattice is more favorable as a substitutional dopant than as an interstitial dopant, although both processes are endothermic. Interstitial Be could potentially exhibit motional averaging from planar to axial symmetry with an activation energy of 0.1 eV. The most stable Bes configuration has Td symmetry with a spin state of S = 1. Co-doping with nitrogen reduces the formation energy of Bes-Nn (n = 1–4) complexes, which further decreases as the number of nitrogen atoms increases. This is attributed to the smaller covalent radius of nitrogen compared to carbon, resulting in reduced lattice distortion. Bes-N3 and Bes-N4 co-doping introduces shallow donors, while Bes exhibits n-type semiconductivity, but the deep donor level renders it impractical for room-temperature applications. These findings provide valuable insights into the behavior of beryllium as a dopant in diamond and highlight the potential of beryllium-nitrogen co-doping for achieving n-type diamond semiconductors.
Copyright (c) 2025 K. M. Etmimi, M. A. Ojalah, A. M. Abotruma https://creativecommons.org/licenses/by/4.0
A computational study of thermoelectric conversion in the PbSexTe1−x semiconductor alloys
The present theoretical study focuses on the structural, electronic and thermoelectric properties of PbTe, PbSe and their ternary alloys PbSexTe1−x, using the density functional theory (DFT) by the full potential linearised augmented plane wave (FP-LAPW) method implemented in Wien2k code. Structural properties were performed by using the generalized gradient approximation of Perdew Burke and Ernzenhof (GGA-PBE) scheme. The results show that the calculated lattice parameters are in good agreement with theoretical data previously obtained. For electronic properties, we noticed that for all the compounds of PbSexTe1−x, we have a direct band gap in L point. For thermoelectric properties, we used BoltzTraP2 code and Gibbs2 code. Our results show that the PbSexTe1−x compounds have reached a value of 2.55 for the figure of merit, which indicates that our material is a good thermoelectric candidate.
Copyright (c) 2025 M. Kaid Slimane, B. N. Brahmi, M. Bouchenaki, S. Bekhechi https://creativecommons.org/licenses/by/4.0
Shape descriptors of equilibrium states in a quantum lattice model with local multi-well potentials: A geometric analysis near the phase transitions in Sn2P2S6 ferroelectric crystals
We analyze the equilibrium states of quantum lattice model with local multi-well potentials for Sn2P2S6 ferroelectric crystals using the mean and Gaussian curvatures (H, K), curvedness (C) and shape index (S). From the energy gap, pressure and temperature variations of H, K, C and S, we have reported the geometric construction of the free energy surfaces for the ferroelectric and paraelectric phases. Their behaviors are explicitly observed near the ferroelectric-paraelectric phase transitions. It is found that H, C and S display a cusp singularity at the criticality while K converges to zero on both sides of the critical and tricritical points.
Copyright (c) 2025 S. Özüm, T. Akkurt, R. Erdem, N. Güçlü https://creativecommons.org/licenses/by/4.0
Absorption and scattering of light by metal-dielectric nanoeggs
The optical and plasmonic properties of metal-dielectric nanoeggs were investigated in this study. Frequency dependencies of polarizability, absorption and scattering cross-sections, and radiation efficiency were determined. Expressions describing the size-dependent behavior of surface plasmon resonance frequencies were derived. The causes of blue and red shifts in the maxima of polarizability, absorption, and scattering cross-sections as well as variations in their number and amplitude were identified. Recommendations were proposed regarding the use of materials with maximum radiation efficiency in different spectral ranges.
absorption and scattering cross-sections
Copyright (c) 2025 A. Korotun, R. Korolkov, R. Malysh, R. Kulykovskyi https://creativecommons.org/licenses/by/4.0
Three-dimensional unfrustrated and frustrated quantum Heisenberg magnets. Specific heat study
We examine the S = 1/2 Heisenberg magnet on four three-dimensional lattices — simple-cubic, diamond, pyrochlore, and hyperkagome ones — for ferromagnetic and antiferromagnetic signs of the exchange interaction in order to illustrate the effect of lattice geometry on the finite-temperature thermodynamic properties with a focus on the specific heat c(T). To this end, we use quantum Monte Carlo simulations or high-temperature expansion series complemented with the entropy method. We also discuss a recent proposal about hidden energy scale in geometrically frustrated magnets.
Copyright (c) 2025 T. Krokhmalskii, T. Hutak, O. Derzhko https://creativecommons.org/licenses/by/4.0
Ab initio study of mechanical and functional properties of novel CaZnC and CaZnSi half-Heusler materials
This research work introduces the DFT through FP-LAPW+lo technique in WIEN2k software to obtain information about structural, thermoelectric, and optoelectronic characteristics of CaZnC and CaZnSi materials. The structural optimization was performed using PBE-GGA functional, while the rest of the characteristics were obtained with the PBE-GGA + TB-mBJ approach. The thermoelectric parameters were evaluated using BoltzTraP software. The elastic constants and other mechanical parameters were computed by utilizing the ELAST code within the WIEN2k software, while the thermodynamic characteristics were evaluated using the Gibbs2 program. The findings show a correlation between atomic composition and lattice dimensions while finding that CaZnC has a direct (Γ–Γ) band gap of 1.186 eV, whereas CaZnSi has an indirect (Γ–X) band gap of 1.067 eV. The optical studies of the compounds show potential applications for photovoltaics while the thermoelectric results find optimized power factors and figure of merit values for energy conversion performance. The elastic parameters of CaZnC and CaZnSi demonstrate material stability and brittleness. Lastly, the thermodynamic evaluations provide information about the thermal mechanism and disorder of the materials. As a result, this research work provides significant advancements in the understanding of the fundamentals of these compounds and highlights their promising applications in renewable energy technologies.
Copyright (c) 2025 P. K. Kamlesh, U. K. Gupta, S. Verma, M. Rani, Y. Toual, A. S. Verma https://creativecommons.org/licenses/by/4.0
Link of the Zitterbewegung with the spin conductivity and the spin-textures of multiband systems
The Zitterbewegung phenomenon in multiband electronic systems is known to be subtly related to the charge conductivity, Berry curvature and the Chern number. Here we show that some spin-dependent properties as the optical spin conductivity and intrinsic spin Hall conductivity are also entangled with the Zitterbewegung amplitudes. We also show that in multiband Dirac-type Hamiltonians, a direct link between the Zitterbewegung and the spin textures and spin transition amplitudes can be established. The later allow us to discern the presence or not of the Zitterbewegung oscillations by simply analyzing the spin or pseudospin textures. We provide examples of the applicability of our approach for Hamiltonian models that show the suppression of specific Zitterbewegung oscillations.
Copyright (c) 2025 F. Mireles, E. Ortiz https://creativecommons.org/licenses/by/4.0
50 years of Yukhnovskii’s critical point theory: its place in the constant flow of theoretical physics
Half a century ago, Ihor Yukhnovskii elaborated a method of studying the critical point of the three-dimensional Ising model based on a layer-by-layer integration in the space of collective variables. His method was an alternative to that based on the ε-expansion for which K. G. Wilson was awarded the Nobel Prize in Physics in 1982. However, Yukhnovskii’s technique, which yielded similar results, provided even deeper insight into the nature of this phenomenon. At that time, we, professor’s students, saw only this aspect of his theory. Later, I realized that the mentioned Yukhnovskii’s work naturally fits into a more general context of the turbulent development of quantum field theory and statistical physics in the last quarter of the twentieth century. The aim of the present article is to look at the main aspects and the impact of Yukhnovskii’s theory from this perspective.
Copyright (c) 2025 Yu. Kozitsky https://creativecommons.org/licenses/by/4.0
Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension d = 3
We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance x as ∼ x - d - σ in a d-dimensional space. It is known to belong to a new long-range random universality class for certain values of the decay parameter σ. Exploiting the field-theoretic renormalization group approach within the minimal subtraction scheme, we compute the three-loop renormalization group functions. On their basis, with the help of asymptotic series resummation methods, we estimate the correlation length critical exponent ν characterising the new universality class for d = 3 and for those values of σ for which long-range interactions are relevant for the critical behaviour.
Copyright (c) 2025 D. Shapoval, M. Dudka https://creativecommons.org/licenses/by/4.0
Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0