Partition function zeros of zeta-urns
DOI:
https://doi.org/10.5488/cmp.27.33601Keywords:
Lee-Yang and Fisher zeroes, critical exponents, first order phase transitions, second order phase transitionsAbstract
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
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