Abstract
The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these algorithm by various methods in order to analyze low-energy excitations for the three-dimensional RFIM with Gaussian distributed disorder that appear in the form of clusters of connected spins. We analyze several properties of these clusters. Our results support the validity of the droplet-model description for the RFIM.
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References
Y. Imry, S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975)
M. Mézard, G. Parisi, M.A. Virasoro, Spin glass theory and beyond (World Scientific, Singapore, 1987)
K.H. Fischer, J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, 1991)
Spin glasses and random fields, edited by A.P. Young (World Scientific, Singapore, 1998)
S. Sabhapandit, D. Dhar, P. Shukla, Phys. Rev. Lett. 88, 197202 (2002)
A. Rosas, S. Coutinho, Physica A 335, 115 (2004)
F. Ye, M. Matsuda, S. Katano, H. Yoshizawa, D.P. Belanger, E.T. Seppala, J.A. Fernandez-Baca, M.J. Alava, J. Magn. Magn. Mat. 272–76 (2004)
F. Colaiori, M.J. Alava, G. Durin, A. Magni, S. Zapperi, Phys. Rev. Lett. 92, (2004)
A. Glaser, A.C. Jones, P.M. Duxbury, Phys. Rev. B 71, (2005)
M. Müller, A. Silva, Phys. Rev. Lett. 96, 117202 (2006)
D.J. Spasojevic, S. Janicevic, M. Knezevic, Europhys. Lett. 76, 912 (2006)
S.H. Lee, H. Jeong, J.D. Noh, Phys. Rev. E 74, 031118 (2006)
D.F. de Albuquerque, I.P. Fittipaldi, J.R. de Sousa, J. Magn. Magn. Mat. 306, 92 (2006)
V.S. Dotsenko, S. Stat. Mech. (2007)
D.M. Silevitch, D. Bitko, J. Brooke, S. Ghosh, G. Aeppli, T.F. Rosenbaum, Nature 448, 567 (2007)
László Környei, Ferenc Iglói, Phys. Rev. E 75, 011131 (2007)
J.J. Moreno, H.G. Katzgraber, A.K. Hartmann, Int. J. Mod. Phys. C 14, 285 (2003)
A. Magni, V. Basso, J. Magn. Magn. Mat. 290, 460 (2005)
Y. Wu, J. Machta, Phys. Rev. Lett. 95, (2005)
V.V. Prudnikov, V.N. Borodikhin, J. Exp. Theor. Phys. 101, 294 (2005)
Y. Wu, J. Machta, Phys. Rev. B 74, (2006)
L. Hernndez, H. Ceva, Physica A 387, 2793 (2008)
N.G. Fytas, A. Malakis, Eur. Phys. J. B 61, 111 (2008)
A.K. Hartmann, A.P. Young, Phys. Rev. B 66, 094419 (2002)
A. Alan Middleton, D.S. Fisher, Phys. Rev. B 65, 134411 (2002)
E.T. Seppälä, A.M. Pulkkinen, M.J. Alava, Phys. Rev. B 66, 144403 (2002)
A.K. Hartmann, Phys. Rev. B 65, 174427 (2002)
I. Dukovski, J. Machta, Phys. Rev. B 67, 014413 (2003)
T. Hamasaki, H. Nishimori, J. Phys. Soc. Jpn 73, 1490 (2004)
M.J. Alava, V. Basso, F. Colaiori, L. Dante, G. Durin, A. Magni, S. Zapperi, Phys. Rev. B 71 (2005)
T. Hamasaki, H. Nishimori, Progr. Theor. Phys. Suppl. 157, 120 (2005)
M. Sarjala, V. Petaja, M. Alava, J. Stat. Mech. (2006)
S.W. Son, H. Jeong, J.D. Noh, Eur. Phys. J. B 50, 431 (2006)
G.E. Santoro, E. Tosatti, J. Phys. A 39, R393 (2006)
Yang Liu, K.A. Dahmen, Phys. Rev. E 76, (2007)
M.B. Hastings, Phys. Rev. Lett. 101, 167206 (2008)
M. Zumsande, M.J. Alava, A.K. Hartmann, J. Stat. Mech. P02012 (2008)
W.L. McMillan, J. Phys. C 17, 3179 (1984)
A.J. Bray, M.A. Moore, Scaling theory of the ordered phase of spin glasses, in Heidelberg Colloquium on Glassy Dynamics, edited by J.L. van Hemmen, I. Morgenstern (Springer, Berlin, 1987), p. 121
D.S. Fisher, D.A. Huse, Phys. Rev. Lett. 56, 1601 (1986)
D.S. Fisher, D.A. Huse, Phys. Rev. B 38, 386 (1988)
A.K. Hartmann, A.P. Young, Phys. Rev. B 64, 180404 (2001)
A.K. Hartmann, M.A. Moore, Phys. Rev. Lett. 90, 12720 (2003)
A.K. Hartmann, M.A. Moore, Phys. Rev. B 69, 104409 (2004)
T. Jörg, J. Lukic, E. Marinari, O.C. Martin. Phys. Rev. Lett. 96, 237205 (2006)
J. Bricomont, A. Kupiainen, Phys. Rev. Lett. 59, 1829 (1987)
T. Nattermann, Spin glasses and Random Fields, edited by P. Young (1998), pp. 277–298
F. Barahona, J. Phys. A 15, 3241 (1982)
A.K. Hartmann, Practical Guide to Computer Simulations (Word Scientific, Singapore, 2009)
A.K. Hartmann, H. Rieger, Optimization Algorithms in Physics (Wiley-VCH, Weinheim, 2001)
M. Preissmann, J.C. Anglès d’Auriac, A. Sebo, J. Math. Comp. Model. 26, 1 1997
H. Rieger, in Advances in Computer Simulation, edited by J. Kertesz, I. Kondor, Lecture Notes in Physics (Springer, Heidelberg, 1998), Vol. 501
C. Moukarzel, M.J. Alava, P.M. Duxbury, H. Rieger, in Phase transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 2001), Vol. 18
M.N.S. Swamy, K. Thulasiraman, Graphs, Networks and Algorithms (Wiley, New York, 1991)
J.D. Claiborne, Mathematical Preliminaries for Computer Networking (Wiley, New York, 1990)
K. Mehlhorn, St. Näher, The LEDA Platform of Combinatorial and Geometric Computing (Cambridge University Press, Cambridge, 1999)
J.-C. Picard, H.D. Ratliff, Networks 5, 357 (1975)
J.L. Träff, Eur. J. Oper. Res. 89, 564 (1996)
R.E. Tarjan, Data Structures and Network Algorithms (Society for Industrial and Applied Mathematics, Philadelphia, 1983)
A.V. Goldberg, R.E. Tarjan, J. ACM 35, 921 (1988)
B. Cherkassky, A. Goldberg, Algorithmica 19, 390 (1997)
A.V. Goldberg, R. Satish, J. ACM 45, 783 (1998)
A.A. Middleton, Phys. Rev. Lett. 88, 017202 (2002)
A.T. Ogielski, Phys. Rev. Lett. 57, 1251 (1986)
A.K. Hartmann, U. Nowak, Eur. Phys. J. B 7, 105 (1999)
The RFIM with a delta-distribution of the random fields (±h) exhibits an exponential ground-state degeneracy
J.-C. Picard, M. Queyranne, Math. Prog. Study 13, 8 (1980)
A.K. Hartmann, Physica A 248, 1 (1998)
S. Bastea, P.M. Duxbury, Phys. Rev. E 58, 4261 (1998)
M. Alava, H. Rieger, Phys. Rev. E 58, 4284 (1998)
D. Fisher, A. Huse, Phys. Rev. B 38, 373 (1988)
A.J. Bray, M.A. Moore, Phys. Rev. Lett. 58, 57 (1987)
Y. Imry, S. Ma, Phys. Rev. Lett. 35, 1399 (1975)
T. Nattermann, Phys. Rev. Lett. 60, 2701 (1988)
J. Sinova, G. Canright, Phys. Rev. B 64, 094402 (2001)
A.K. Hartmann, A.J. Bray, A.C. Carter, M.A. Moore, A.P. Young, Phys. Rev. B 66, 224401 (2002)
A.K. Hartmann, A.P. Young, Phys. Rev B 65, 094419 (2002)
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Zumsande, M., Hartmann, A. Low-energy excitations in the three-dimensional random-field Ising model. Eur. Phys. J. B 72, 619–627 (2009). https://doi.org/10.1140/epjb/e2009-00410-2
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DOI: https://doi.org/10.1140/epjb/e2009-00410-2