Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice

Shigetoshi Katsura and Izuru Nagahara

Physica A: Statistical Mechanics and its Applications, 1980, vol. 104, issue 3, 397-416

Abstract: The energies and the entropies of the spin-glass state and the paramagnetic state at T = 0 of the random-bond Ising mixture of the ferromagnetic bond (concentration p) and the antiferromagnetic bond (concentration 1 − p) on the square lattice are calculated by the method of the square approximation in the simple version. A self-consistent relation that the partial trace of the normalized density matrix of the square cluster is equal to that of the vertex (tr(jklϱ̂(4)(i,j,k,l) = ϱ̂(1)(i)) leads to an integral equation for the distribution function of the effective fields, and it is solved exactly at T = 0. The symmetric solution of the integral equation contains the paramagnetic state and two spin-glass states, SG1 and SG2. The energies and the entropies of these states are obtained as functions of the concentration p. The values of the energies per spin at p = 12 are -0.75|EF|, -0.72746|EF|, -0.72543|EF|, and correspond to a minimum, a saddle point, and a maximum, respectively, and the values of the entropies are 0, 0.082886kB, and 0.054457kB, respectively. The present results are compared with those of the pair approximation and discussed.

Date: 1980
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:104:y:1980:i:3:p:397-416

DOI: 10.1016/0378-4371(80)90003-5

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