Abstract.
The three-dimensional bimodal random-field Ising model is investigated using the N-fold version of the Wang-Landau algorithm. The essential energy subspaces are determined by the recently developed critical minimum energy subspace technique, and two implementations of this scheme are utilized. The random fields are obtained from a bimodal discrete (±Δ) distribution, and we study the model for various values of the disorder strength Δ, Δ=0.5,1,1.5 and 2, on cubic lattices with linear sizes L=4–24. We extract information for the probability distributions of the specific heat peaks over samples of random fields. This permits us to obtain the phase diagram and present the finite-size behavior of the specific heat. The question of saturation of the specific heat is re-examined and it is shown that the open problem of universality for the random-field Ising model is strongly influenced by the lack of self-averaging of the model. This property appears to be substantially depended on the disorder strength.
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References
Y. Imry, S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975)
T. Nattermann, J. Villain, in Phase Transitions 11, 5 (1988)
D.P. Belanger, A.P. Young, J. Magn. Magn. Mater. 100, 272 (1991)
H. Rieger, Annual Reviews of Computational Physics II, edited by D. Stauffer (Singapore, World Scientific, 1995)
D.P. Belanger, T. Nattermann, in Spin Glasses and Random Fields, edited by A.P. Young (Singapore, World Scientific, 1998)
A.K. Hartmann, A.P. Young, Phys. Rev. B 64, 214419 (2001)
A.K. Hartmann, U. Nowak, Eur. Phys. J. B 7, 105 (1999)
M.E.J. Newman, G.T. Barkema, Phys. Rev. E 53, 393 (1996)
N. Sourlas, Comput. Phys. Commun. 121, 183 (1999)
G. Parisi, N. Sourlas, Phys. Rev. Lett. 43, 744 (1979)
G. Grinstein, S.-K. Ma, Phys. Rev. Lett. 49, 685 (1982); Phys. Rev. B 28, 2588 (1983)
J.Z. Imbrie, Phys. Rev. Lett. 53, 1747 (1984)
J. Bricmont, A. Kupiainen, Phys. Rev. Lett. 59, 1829 (1987)
H. Rieger, Phys. Rev. B 52, 6659 (1995)
J. Villain, J. Phys. Lett. France 46, 1843 (1985)
D.S. Fisher, Phys. Rev. Lett. 56, 416 (1985)
A.J. Bray, M.A. Moore, J. Phys. C 18, 927 (1985)
A.T. Ogielski, D.A. Huse, Phys. Rev. Lett. 56, 1298 (1986)
A.T. Ogielski, Phys. Rev. Lett. 57, 1251 (1986)
S.R. McCay, A.N. Berker, J. Appl. Phys. 64, 5785 (1988)
A. Aharony, Phys. Rev. B 18, 3318 (1978)
J.T. Chayes, L. Chayes, D.S. Fisher, T. Spencer, Phys. Rev. Lett. 57, 2999 (1986)
J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, 1996)
A.B. Harris, J. Phys. C 7, 1671 (1976)
M. Itakura, Phys. Rev. B 64, 012415 (2001)
M. Mézard, A.P. Young, Europhys. Lett. 18, 653 (1992)
M. Mézard, R. Monasson, Phys. Rev. B 50, 7199 (1994)
J.-C. Anglés d'Auriac, N. Sourlas, Europhys. Lett. 39, 473 (1997)
A. Malakis, N.G. Fytas, Phys. Rev. E 73, 016109 (2006)
N.G. Fytas, A. Malakis, Eur. Phys. J. B 50, 39 (2006)
H. Rieger, A.P. Young, J. Phys. A 26, 5279 (1993)
U. Nowak, K.D. Usadel, J. Esser, Physica A 250, 1 (1998)
A.A. Middleton, D.S. Fisher, Phys. Rev. B 65, 134411 (2002)
S. Fishman, A. Aharony, J. Phys. C 12, 729 (1979)
J. Cardy, Phys. Rev. B 29, 505 (1985)
D.P. Belanger, A.R. King, V. Jaccarino, J.L. Cardy, Phys. Rev. B 28, 2522 (1983)
M. Hagen, R.A. Cowley, S.K. Satija, H. Yoshizawa, G. Shirane, R.J. Birgeneau, H.J. Guggenheim, Phys. Rev. B 28, 2602 (1983)
D.P. Belanger, A.R. King, V. Jaccarino, Phys. Rev. B 31, 4538 (1985); P. Pollack, W. Kleeman, D.P. Belanger, Phys. Rev. B 38, 4773 (1988)
W.C. Barber, D.P. Belanger, J. Magn. Magn. Mater. 226, 545 (2001)
M. Karszewiski, J. Kushauer, Ch. Binek, W. Kleeman, D. Bertrand, J. Phys. C 6, 75 (1994)
G. Grinstein, Phys. Rev. Lett. 37, 944 (1976); M. Schwartz, A. Soffer, Phys. Rev. Lett. 55, 2499 (1985); I. Dayan, M. Schwartz, A.P. Young, J. Phys. A 26, 3093 (1993)
A. Malakis, A. Peratzakis, N.G. Fytas, Phys. Rev. E 70, 066128 (2004); A. Malakis, S.S. Martinos, I.A. Hadjiagapiou, N.G. Fytas, P. Kalozoumis, Phys. Rev. E 72, 066120 (2005)
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)
M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford, Clarendon Press, 1999)
A.P. Young, M. Nauenburg, Phys. Rev. Lett. 54, 2429 (1986)
I. Dukovski, J. Machta, Phys. Rev. B 67, 014413 (2003)
N.M.S. Swamy, K. Thulasiraman, Graphs, Networks and Algorithms (New York, Wiley, 1990)
Y. Wu, J. Machta, Phys. Rev. Lett. 95, 137208 (2005)
V.S. Dotsenko, W. Selke, A.L. Talapov, Physica A 170, 278 (1991)
U. Wolff, Phys. Rev. Lett. 62, 361 (1989)
A.M. Ferrenberg, R.H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988); Phys. Rev. Lett. 63, 1195 (1989)
R.H. Swendsen, J.-S. Wang, Phys. Rev. Lett. 57, 2607 (1986)
O. Redner, J. Machta, L.F. Chayes, Phys. Rev. E 58, 2749 (1998); L. Chayes, J. Machta, O. Redner, J. Stat. Phys. 93, 17 (1998)
J. Machta, M.E.J. Newman, L.B. Chayes, Phys. Rev. E 62, 8782 (2000)
A. Malakis, S.S. Martinos, I.A. Hadjiagapiou, A.S. Peratzakis, Int. J. Mod. Phys. C 15, 729 (2004)
J. Lee, Phys. Rev. Lett. 71, 211 (1993)
B.A. Berg, T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992)
A.R. Lima, P.M.C. de Oliveira, T.J.P. Penna, J. Stat. Phys. 99, 961 (2000)
F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001); Phys. Rev. E 64, 056101 (2001); D.P. Landau, F. Wang, Comput. Phys. Commun. 147, 674 (2002)
B.J. Schulz, K. Binder, M. Muller, Int. J. Mod. Phys. C 13, 447 (2002)
P.M.C. de Oliveira, T.J.P. Penna, H.J. Herrmann, Braz. J. Phys. 26, 677 (1996)
C. Zhou, R.N. Bhatt, Phys. Rev. E 72, 025701(R) (2005)
G. Parisi, N. Sourlas, Phys. Rev. Lett. 89, 257204 (2002)
K. Binder, D.W. Heermann, Monte Carlo Simulations in Statistical Physics (Berlin, Springer-Verlag, 1988)
S. Wiseman, E. Domany, Phys. Rev. E 52, 3469 (1995); Phys. Rev. Lett. 81, 22 (1998)
A. Aharony, A.B. Harris, Phys. Rev. Lett. 77, 3700 (1996)
D.P. Landau, in Finite Size Scaling and Numerical Simulations of Statistical systems, edited by V. Privman (Singapore, World Scientific, 1990)
R. Hilfer, B. Biswal, H.G. Mattutis, W. Janke, Phys. Rev. E 68, 046123 (2003)
K. Eichhorn, K. Binder, J. Phys. C 8, 5209 (1996)
L.W. Bernard, S. Prakash, I.A. Campbell, Phys. Rev. Lett. 77, 2798 (1996)
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Malakis, A., Fytas, N. Thermal critical behavior and universality aspects of the three-dimensional random-field Ising model. Eur. Phys. J. B 51, 257–266 (2006). https://doi.org/10.1140/epjb/e2006-00219-5
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DOI: https://doi.org/10.1140/epjb/e2006-00219-5