Partition function zeros of zeta-urns

Authors

DOI:

https://doi.org/10.5488/cmp.27.33601

Keywords:

Lee-Yang and Fisher zeroes, critical exponents, first order phase transitions, second order phase transitions

Abstract

We discuss the distribution of partition function zeros for the grand-canonical ensemble of the zeta-urn model, where tuning a single parameter can give a first or any higher order condensation transition. We compute the locus of zeros for finite-size systems and test scaling relations describing the accumulation of zeros near the critical point against theoretical predictions for both the first and higher order transition regimes.

References

Bialas P., Burda Z., Johnston D., Nucl. Phys. B, 1997, 493, 505–516. DOI: https://doi.org/10.1016/S0550-3213(97)00192-2

Bialas P., Burda Z., Johnston D., Phys. Rev. E, 2023, 108, 064107. DOI: https://doi.org/10.1103/PhysRevE.108.064108

Drouffe J.-M., Godrèche C., Camia F., J. Phys. A: Math. Gen., 1998, 31, L19. DOI: https://doi.org/10.1088/0305-4470/31/1/003

Bialas P., Burda Z., Johnston D., Nucl. Phys. B, 1999, 542, 413–424. DOI: https://doi.org/10.1016/S0550-3213(98)00842-6

Godrèche C., Lect. Notes Phys., 2007, 716, 261–294. DOI: https://doi.org/10.59962/9780774851640-024

Evans M. R., Braz. J. Phys., 2000, 30, 42–57. DOI: https://doi.org/10.1590/S0103-97332000000100005

Evans M. R., Hanney T., J. Phys. A: Math. Gen., 2005, 38, R195. DOI: https://doi.org/10.1088/0305-4470/38/19/R01

Grosskinsky S., Schütz G. M., Spohn H., J. Stat. Phys., 2003, 113, 389-410. DOI: https://doi.org/10.1023/A:1026008532442

Godréche C., Luck J. M., J. Phys. A: Math. Gen., 2005, 38, 7215. DOI: https://doi.org/10.1088/0305-4470/38/33/002

Waclaw B., Bogacz L., Burda Z., Janke W., Phys. Rev. E, 2007, 76, 046114. DOI: https://doi.org/10.1103/PhysRevE.76.046114

Majumdar S. N., Evans M. R., Zia R. K. P., Phys. Rev. Lett., 2005, 94, 180601. DOI: https://doi.org/10.1103/PhysRevLett.94.180601

Evans M. R., Majumdar S. N., Zia R. K. P., J. Stat. Phys., 2006, 123, 357–390. DOI: https://doi.org/10.1007/s10955-006-9046-6

Evans M. R., Majumdar S. N., Zia R. K. P., J. Phys. A: Math. Gen., 2006, 39, 4859. DOI: https://doi.org/10.1088/0305-4470/39/18/006

Janson S., Probab. Surveys, 2012, 9, 103–252. DOI: https://doi.org/10.1214/11-PS188

Bialas P., Burda Z., Phys. Lett. B, 1996, 384, 75–80. DOI: https://doi.org/10.1016/0370-2693(96)00795-2

Bialas P., Burda Z., Waclaw B., AIP Conf. Proc., 2005, 776, 14–28.

Godrèche C., J. Phys. A: Math. Theor., 2017, 50, 195003. DOI: https://doi.org/10.1088/1751-8121/aa6a6e

Yang C. N., Lee T. D., Phys. Rev., 1952, 87, 404. DOI: https://doi.org/10.1103/PhysRev.87.404

Yang C. N., Lee T. D., Phys. Rev., 1952, 87, 410. DOI: https://doi.org/10.1103/PhysRev.87.410

Fisher M. E., In: Lecture in Theoretical Physics, Vol. VIIC, Brittin W. E. (Ed.), Gordon and Breach, New York, 1968, 1.

Bena I., Droz M., Lipowski A., Int. J. Mod. Phys. B, 2005, 19, 4269–4329. DOI: https://doi.org/10.1142/S0217979205032759

Grossmann S., Resenhauer W., Z. Phys., 1967, 207, 138–152. DOI: https://doi.org/10.1007/BF01326224

Abe R., Prog. Theor. Phys., 1967, 37, 1070–1079. DOI: https://doi.org/10.1143/PTP.37.1070

Abe R., Prog. Theor. Phys., 1967, 38, 72–80. DOI: https://doi.org/10.1143/PTP.38.72

Abe R., Prog. Theor. Phys., 1967, 38, 322–331. DOI: https://doi.org/10.1143/PTP.38.322

Abe R., Prog. Theor. Phys., 1967, 38, 568–575. DOI: https://doi.org/10.1143/PTP.38.568

Suzuki M., Prog. Theor. Phys., 1967, 38, 289–290. DOI: https://doi.org/10.1143/PTP.38.289

Suzuki M., Prog. Theor. Phys., 1967, 38, 1225–1242. DOI: https://doi.org/10.1143/PTP.38.1225

Suzuki M., Prog. Theor. Phys., 1967, 38, 1243–1251. DOI: https://doi.org/10.1143/PTP.38.1243

Suzuki M., Prog. Theor. Phys., 1968, 39, 349–364. DOI: https://doi.org/10.1143/PTP.39.349

Janke W., Johnston D. A., Kenna R., Nucl. Phys. B, 2006, 736, 319–328. DOI: https://doi.org/10.1016/j.nuclphysb.2005.12.013

Ferrari P. A., Landim C., Sisko V. V., J. Stat. Phys., 2007, 128, 1153-1158. DOI: https://doi.org/10.1007/s10955-007-9356-3

Chleboun P., Grosskinsky S., J. Stat. Phys., 2010, 140, 846–872. DOI: https://doi.org/10.1007/s10955-010-0017-6

Armendariz I., Grosskinsky S., Loulakis M., Stochastic Processes Appl., 2013, 123, 3466–3496. DOI: https://doi.org/10.1016/j.spa.2013.04.021

Chleboun P., Grosskinsky S., J. Stat. Phys., 2014, 154, 432–465. DOI: https://doi.org/10.1007/s10955-013-0844-3

Jatuviriyapornchai W., Chleboun P., Grosskinsky S., J. Stat. Phys., 2020, 178, 682–710. DOI: https://doi.org/10.1007/s10955-019-02451-9

Godrèche C., J. Stat. Phys., 2021, 182, 13. DOI: https://doi.org/10.1007/s10955-020-02679-w

Blythe R. A., Evans M. R., Phys. Rev. Lett., 2002, 89, 080601. DOI: https://doi.org/10.1103/PhysRevLett.89.080601

Blythe R. A., Evans M. R., Braz. J. Phys., 2003, 33, 464. DOI: https://doi.org/10.1590/S0103-97332003000300008

Blythe R. A., Janke W., Johnston D. A., Kenna R., J. Stat. Mech., 2004, P06001. DOI: https://doi.org/10.1088/1742-5468/2004/06/P06001

Blythe R. A., Janke W., Johnston D. A., Kenna R., J. Stat. Mech., 2004, P10007. DOI: https://doi.org/10.1088/1742-5468/2004/10/P10007

Deger A., Brange F., Flindt C., Phys. Rev. B, 2020, 102, 174418. DOI: https://doi.org/10.1103/PhysRevB.102.174418

Vecsei P. M., Lado J. L., Flindt C., Phys. Rev. B, 2022, 106, 054402. DOI: https://doi.org/10.1103/PhysRevB.106.054402

Downloads

Published

2024-09-24

Issue

Vol. 27 No. 3 (2024): Special issue “Statistical physics and emergent behaviour: from spin models to cultural complexity”

Section

Articles

Categories

License

Copyright (c) 2024 P. Bialas, Z. Burda, D. A. Johnston

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC

How to Cite

[1]
P. Bialas, Z. Burda, and D. A. Johnston, “Partition function zeros of zeta-urns”, Condens. Matter Phys., vol. 27, no. 3, p. 33601, Sep. 2024, doi: 10.5488/cmp.27.33601.