Reentrant ferromagnetism in a two‐dimensional Ising model with random nearest‐neighbor interactions (abstract)

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Reentrant ferromagnetism in a twodimensional Ising model with random nearest neighbor interactions (abstract)

N. Benayad, A. Benyoussef, and N. Boccara

Citation: Journal of Applied Physics 63, 4001 (1988); doi: 10.1063/1.340578 View online: http://dx.doi.org/10.1063/1.340578

View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/63/8?ver=pdfcov Published by the AIP Publishing

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Phase diagram for the Bethe lattice spin glass (abstract)

J. M. Carlson,a) J. T. Chayes,b),C) L. Chayes,C),d) and J. P. Sethnaa)

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853 D. J. Thouless^G)

Department of Physics, University of Washington, Seattle, Washingon 98195

We present the results of rigorous calculations for the ± J Ising spin-glass model on the Bethe lattice. The phase diagram for varying temperature and fraction of ferromagnetic bonds is derived near the paramagnetic phase boundary. In addition to the spin-glass and paramagnetic phases, we find a nontrivial ferromagnetic phase and a magnetized spin-glass phase,

characterized by diverging Edwards-Anderson susceptibility. The recursion relation for the distribution of single-site magnetizations is studied as a dynamical system on an appropriate function space, the bulk thermodynamics is described by the attractors of the recursion relation, and the phase transitions correspond to bifurcations in the dynamics. Using bifurcation theory, we establish the existence of a stable distribution of single-site

magnetizations near the paramagnetic phase boundary. At least in single-site properties, the existence proof precludes chaos, and infinite hierarchy of transitions, and other conceivable bizarre possibilities. While our phase diagram is very similar to the phase diagram for the Sherrington-Kirkpatrick model, the Bethe lattice provides a useful description of the mean- field behavior of spin glasses because the interactions are short range, the analysis is much more straightforward, and the results have been made completely rigorous.

a) Supported by NSF grant No. DMR-8503544.

h) Supported by NSf' grant No. DMR-8314625.

c) Supported by DOE grant No. DE-AC02-83ER13044.

d) Supported by NSF grant No. DMR-83 19301.

e) Current address: Department of Mathematics, UCLA, Los Angeles, CA 90024.

Reentrant ferromagnetism in a two .. dimensional Ising model with random nearest .. neighbor interactions (abstract)

N. Benayad and A. Benyoussef

Lab. Magnetisme, Faculte des Sciences. Rabat, Morocco N. Boccara

DPhG/PSRM, CEN Saclay, France and Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60680

Reentrant behavior seems to be characteristic of systems with competing interactions even when no spin-glass phase exists. Using various methods (finite duster approximation,! mean- field renormalization,2 finite cluster renormalization, etc.) we determined the phase diagram of a two-dimensional square Ising model with random nearest-neighbor interactions Jij

distributed according to P(Jij) = (1 - p)l5(Jij - J)

+

pl5(Jij - aJ}, where J>O and 0> a > - 1. Such a model has been considered by Wolff and Zittartz.³These authors

discussed its qualitative features and argued that a reentrant behavior should be observed. OUf

calculations agree with this conjecture,

This paper was not proofread by the author; however. it has been proofread by one of the Publication Chairpersons.

'N. Boccara, Phys. Lett. 94A, 185 (1979).

2J. O. Indekeu. A. Maritan, A. L. Stella J. Phys. A 15, L291 (1982).

3W. F. Wollfand J. Zittartz, Z. Phys. B 60,185 (1985).

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