Abstract
We provide a formula and an upper bound for the average over the disorder of the pair correlation function of ±J Ising spin glasses by using the symmetries of the system, We show the decay of the mean spin pair correlation function when the proportion of antiferromagnetic bonds is larger than the critical parameter associated with the pair dissociation phase transition.
Similar content being viewed by others
REFERENCES
Biggs, N. Algebraic graph theory (Cambridge, 1992).
Binder, K., and Young, A. P. Spin glasses: Experimental facts, theoretical concepts, and open problems, Reviews of Modern Physics 58(4) (1986).
Carlson, J. M., Chayes, J. T., Chayes, L., Setha, D. J., and Thouless, D. J. Bethe Lattice Spin Glasses: The Effects of a Ferromagnetic Bias and External Fields, J. Stat. Phys. 61(5/6):987–1067 (1990).
Cataudella, V. Percolation transition in systems with frustration, Physica A 183:249–254 (1991).
Cataudella, V., Franzese, G., Nicodemi, M., and Scola, A. Critical clusters and efficient dynamics for frustrated spin models, Phys. Rev. Letters 72(10):1541–1544 (1994).
Coniglio, A., di Liberto, F., Monrey, G., and Peruggi, F. Phys. Rev. B. 44:12605 (1991).
Fradkin, E., Huberman, B. A., and Shenker, S. H. Gauge symmetries in random magnetic systems, Physical Review B 8(9):4789–4814 (1978).
Gandolfi, A., Keane, M. S., and Newman, C. M. Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses, Probability Theory and Related Fields 92:511–527 (1992).
Gandolfi, A. A remark on gauge symmetries in Ising spin glasses. Preprint, 1997.
Imaoka, Ikeda, and Kasai, Percolation transition in two dimensional ±J Ising spin glasses, Physica A 246:18–26 (1997).
Kasai, J., and Okiji, A. Percolation problem describing ±J Ising spin glasses system, Progress of Theoretical Physics 79(5) (1988).
Katsura, S. Glass like phase and the close packed lattices, Physica A 88A:583–590 (1977).
Kolan, A. J., and Palmer, R. G. Distribution of frustrated plaquettes in the random bond square lattice, J. Phys. C: Solid St. Phys. 13:L575–80 (1980).
Mazza, C. Gauge symmetries and percolation in ±J Ising spin glasses. Preprint, 1997. To appear in Probability Theory and Related Fields.
Liebman and Schuster, Correlation between frustrated plaquettes in the random bond square lattice, J. Phys. C: Solid St. Phys. 14:709–716 (1981).
Newman, C. M. Ising models and dependent percolation, in Topics in Statistical Dependence, Institute of Mathematical Statistics, Lecture notes No. 16 (1990).
Newman, C. M. Disordered Ising systems and random cluster representation, in Probability and phase transition, G. Grimmett, ed. (NATO ASI Series, Vol. 420, Serie C, 1994).
Nishimori, H. Exact results and critical properties of the Using model with competing interactions, J. Phys. C: Solid St. Phys. 13:4071–6 (1980).
Roman, S. Coding and Information Theory (Springer, 1992).
Schuster, H. G. Phase transitions in the frustration network, Z. Physik B35:163–170 (1979).
van der Waerden, B. L. Die lange Reichweite der regelmassigen Atomanordnung in Mischkristallen, Z. Physik 118:473 (1941).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mazza, C. On the Mean Pair Correlation Function of ±J Ising Spin Glasses. Journal of Statistical Physics 92, 559–569 (1998). https://doi.org/10.1023/A:1023036520918
Issue Date:
DOI: https://doi.org/10.1023/A:1023036520918