On the phase diagram of the random field Ising model on the Bethe lattice

Journal of Statistical Physics

Volumn 93, Issue 1-2, 1998, Pages 33-78

  Bleher, P M ^a   Ruiz, J ^b   Zagrebnov, V A ^b,c  

^a INDIANA UNIVERSITY   (United States)

^b CNRS   (France)

^c AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Bethe lattice; Dipole configurations; Gibbs states; Griffiths singularities; Ground states; Ising model; Random external field; Residual entropy

Indexed keywords

EID: 0032178165     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000026727.43077.49     Document Type: Article

References (17)

1. G. Aeppli and R. Bruinsma, Linear response theory and the one-dimensional Ising ferromagnet in a random-field, Phys. Lett. A 97:117-120 (1983).
2. R. J. Baxter, Exactly Solvable Models in Statistical Mechanics (Academic Press, London, 1982).
3. U. Behn, V. B. Priezzhev, and V. A. Zagrebnov, One-dimensional random field Ising model: Residual entropy, magnetization, and the "Perestroyka" of the ground state, Physica A 167:481-493 (1990).
4. P. M. Bleher, J. Ruiz, and V. A. Zagrebnov, On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice, J. Stat. Phys. 79:473-482 (1995).
5. P. M. Bleher, J. Ruiz, and V. A. Zagrebnov, One-dimensional random-field Ising model: Gibbs states and structure of ground states. J. Stat. Phys. 84:1077-1093 (1996).
6. P. M. Bleher and N. N. Ganihodgaev, On pure phases of the Ising model on the Bethe lattice, Theory Prob. Appl. 35:1-26 (1990).
7. R. Bruinsma, Random field Ising model on a Bethe lattice, Phys. Rev. B 30:289-299 (1984).
8. R. Bruinsma and G. Aeppli, One-dimensional Ising model in a random field, Phys. Rev. Lett. 50:1494-1497 (1983).
9. B. Derrida, J. Vannimenus, and Y. Pommeau, Simple frustated systems: Chains, strips and squares. J. Phys. C: Solid State Phys. 11:4749-4765 (1978).
10. M. Campanino and A. C. D. van Enter, Weak versus strong uniqueness of Gibbs measures: A regular short range example, J. Math. A: Math. Gen. 28:L45-L47 (1995).
11. A. C. D. van Enter, On the set of pure states for some systems with non-periodic long-range order, Physica A 232, 600-607 (1996).
12. C. M. Fortuin, P. W. Kasteleyn, and J. Ginibre, Correlation inequalities on some partially ordered sets. Commun. Math. Phys. 22, 89-103 (1971).
13. H. O. Georgii, Gibbs Measures and Phases Transitions (de Gruyter, Berlin, 1988).
14. S. Katsura and N. Miyamoto, Random Ising model in the magnetic field at T = 0, Physica A 112:393-404 (1982).
15. J. L. Lebowitz and A. Martin-Löf, On the uniqueness of the equilibrium state for Ising spin systems, Commun. Math. Phys. 25:276-282 (1972).
16. M. Puma and J. F. Fernandez, Entropy of a random-bond Ising chain, Phys. Rev. B 18:1391-1394 (1978).
17. A. Vilenkin, Random Ising model chain in a magnetic field at low temperatures, Phys. Rev. B 18:1474-1478 (1978).