Abstract
A Potts glass model proposed by Nishimori and Stephen [H. Nishimori, M.J. Stephen, Phys. Rev. B 27, 5644 (1983)] is analyzed by means of the replica mean field theory. This model is a discrete model, has a gauge symmetry, and is called the Potts gauge glass model. By comparing the present results with the results of the conventional Potts glass model, we find the coincidences and differences between the models. We find a coincidence that the property for the Potts glass phase in this model is coincident with that in the conventional model at the mean field level. We find a difference that, unlike in the case of the conventional p-state Potts glass model, this system for large p does not become ferromagnetic at low temperature under a concentration of ferromagnetic interaction. The present results support the act of numerically investigating the present model for study of the Potts glass phase in finite dimensions.
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References
J. Jäckle, Rep. Prog. Phys. 49, 171 (1986)
Proceedings of the First International Meeting on Relaxations in Complex Systems, edited by K.L. Ngai, J. Non-Cryst. Solids 131-133 (1991)
W. Götze, J. Sjögren, Rep. Progr. Phys. 55, 214 (1992)
Proceedings of the Second International Discussion Meeting on Relaxations in Complex System, edited by K.L. Ngai, J. Non-Cryst. Solids 172-174 (1994)
Proceedings of the Third International Discussion Meeting on Relaxations in Complex Systems, edited by K.L. Ngai, Non-Cryst. Solids 235-237 (1998)
K. Binder, J. Baschnagel, W. Kob, W. Paul, Bridging Time Scales: Molecular Simulations for the Next Decade, Lecture Notes in Physics (Springer-Verlag, 2002), Vol. 605, p. 199
P. Ginsparg, Y.Y. Goldschmidt, J.-B. Zuber, Nucl. Phys. B 170, 409 (1980)
H. Nishimori, M.J. Stephen, Phys. Rev. B 27, 5644 (1983)
E. Marinari, S. Mossa, G. Parisi, Phys. Rev. B 59, 8401 (1999)
D. Elderfield, D. Sherrington, J. Phys. C 16, L497 (1983)
D. Elderfield, D. Sherrington, J. Phys. C 16, L971 (1983)
D. Elderfield, D. Sherrington, J. Phys. C 16, L1169 (1983)
D.J. Gross, I. Kanter, H. Sompolinsky, Phys. Rev. Lett. 55, 304 (1985)
T.R. Kirkpatrick, P.G. Wolynes, Phys. Rev. B 36, 8552 (1987)
T.R. Kirkpatrick, D. Thirumalai, Phys. Rev. B 37, 5342 (1988)
D. Thirumalai, T.R. Kirkpatrick, Phys. Rev. B 38, 4881 (1988)
G. Cwilich, T.R. Kirkpatrick, J. Phys. A 22, 4971 (1989)
E. De Santis, G. Parisi, F. Ritort, J. Phys. A 28, 3025 (1995)
D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975)
H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford University Press, 2001)
D.M. Carlucci, Phys. Rev. B 60, 9862 (1999)
C. Yamaguchi, Prog. Theor. Phys. 127, 199 (2012)
A. Honecker, J.L. Jacobsen, M. Picco, P. Pujol, Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como, 2001
J.L. Jacobsen, M. Picco, Phys. Rev. E 65, 026113 (2002)
H. Nishimori, K. Nemoto, J. Phys. Soc. Jpn 71, 1198 (2002)
M. Ohzeki, H. Nishimori, A.N. Berker, Phys. Rev. E 77, 061116 (2008)
M. Ohzeki, J.L. Jacobsen, J. Phys. A 48, 095001 (2015)
P.L. Doussal, A.B. Harris, Phys. Rev. Lett. 61, 625 (1988)
A. Erzan, E.J.S. Lage, J. Phys. C 16, L555 (1983)
V. Janiš, A. Klíč, J. Phys.: Condens. Matter 23, 022204 (2011)
V. Janiš, A. Klíč, Phys. Rev. B 84, 064446 (2011)
A. Cruz, L.A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, A.M. Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J.J. Ruiz-Lorenzo, S.F. Schifano, D. Sciretti, A. Tarancon, R. Tripiccione, J.L. Velasco, D. Yllanes, A.P. Young, Phys. Rev. B 79, 184408 (2009)
R.A. Baños, A. Cruz, L.A. Fernandez, A. Gordillo-Guerrero, J.M. Gil-Narvion, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A.M. Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J.J. Ruiz-Lorenzo, B. Seoane, S.F. Schifano, A. Tarancon, R. Tripiccione, D. Yllanes, J. Stat. Mech. 2010, P05002 (2010)
C. Brangian, W. Kob, K. Binder, J. Phys. A 36, 10847 (2003)
C. Brangian, W. Kob, K. Binder, Europhys. Lett. 59, 546 (2002)
L.W. Lee, H.G. Katzgraber, A.P. Young, Phys. Rev. B 74, 104416 (2006)
T. Takahashi, K. Hukushima, Phys. Rev. E 91, 020102 (2015)
Y.Y. Goldschmidt, J. Phys. A 22, L157 (1989)
L. Viana, A.J. Bray, J. Phys. C 18, 3037 (1985)
H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981)
F. Caltagirone, G. Parisi, T. Rizzo, Phys. Rev. E 85, 051504 (2012)
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Yamaguchi, C. A curious relationship between Potts glass models. Eur. Phys. J. B 88, 195 (2015). https://doi.org/10.1140/epjb/e2015-60068-7
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DOI: https://doi.org/10.1140/epjb/e2015-60068-7