Abstract
We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) q-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., q = 3, 4, and q = 8, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point.
Similar content being viewed by others
References
D.B. Abraham, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 1986), Vol. 10
S. Dietrich, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 1988), Vol. 12
W. Selke, W. Pesch, Z. Phys. B 47, 335 (1982)
W. Selke, D.A. Huse, Z. Phys. B 50, 113 (1983)
M.E. Fisher, J. Stat. Phys. 34, 667 (1984)
W. Selke, J.M. Yeomans, J. Phys. A 16, 2789 (1983)
W. Selke, D.A. Huse, D.M. Kroll, J. Phys. A 17, 3019 (1984)
A. Yamagata, K. Kasano, Z. Phys. B 87, 219 (1992)
E. Carlon, F. Igloi, W. Selke, F. Szalma, J. Stat. Phys. 96, 531 (1999)
E.V. Albano, K. Binder, Phys. Rev. E 85, 061601 (2012)
N.G. Fytas, W. Selke, Eur. Phys. J. B 86, 365 (2013)
M.L. Trobo, E.V. Albano, Eur. Phys. J. B 87, 303 (2014)
E.V. Albano, K. Binder, J. Stat. Phys. 157, 436 (2014)
J. Bricmont, J.L. Lebowitz, J. Stat. Phys. 46, 1015 (1987)
A. Messager, S. Miracle-Sole, J. Ruiz, S. Shlosman, Commun. Math. Phys. 140, 275 (1991)
J. Cardy, Nucl. Phys. B 565, 506 (2000)
G. Delfino, A. Squarcini, Ann. Phys. 342, 171 (2014)
F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982)
W. Kinzel, E. Domany, Phys. Rev. B 23, 3421 (1981)
B. Berche, C. Chatelain, in Order, Disorder, and Criticality: Advanced Problems of Phase Transition Theory, edited by Y. Holovatch (World Scientific, Singapore, 2004), Vol. 1, pp. 147–199
C. Monthus, T. Garel, Phys. Rev. B 77, 134416 (2008)
A. Brener, Diploma Thesis, RWTH Aachen University, 2010
D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (University Press, Cambridge, 2005)
A. Gamsa, J. Cardy, J. Stat. Mech. 2007, P08020 (2007)
S. Chen, A.M. Ferrenberg, D.P. Landau, Phys. Rev. E 52, 1377 (1994)
J. Cardy, J.L. Jacobsen, Phys. Rev. Lett. 79, 4063 (1997)
C. Chatelain, B. Berche, Phys. Rev. Lett 80, 1670 (1997)
G. Palagyi, C. Chatelain, B. Berche, F. Igloi, Eur. Phys. J. B 13, 357 (1999)
J.L. Jacobsen, M. Picco, Phys. Rev. E 61, R13(R) (2000)
Vl.S. Dotsenko, V.A. Fateev, Nucl. Phys. B 240, 312 (1984)
V. Privman, P.C. Hohenberg, A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 1991), Vol. 14, p. 1
L.N. Shchur, B. Berche, P. Butera, Phys. Rev. B 77, 144410 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fytas, N.G., Malakis, A., Selke, W. et al. Interfacial adsorption in Potts models on the square lattice. Eur. Phys. J. B 88, 204 (2015). https://doi.org/10.1140/epjb/e2015-60326-8
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2015-60326-8