The asymmetric continuous distribution function of the effective field of the Ising model in the spin glass and the ferromagnetic states on the Bethe lattice

Mitsuhiro Sasaki and Shigetoshi Katsura

Physica A: Statistical Mechanics and its Applications, 1989, vol. 157, issue 3, 1195-1202

Abstract: The distribution of effective fields of the Ising spin glass on the Bethe lattice at T=0 is obtained for a general concentration p of ±J bonds, by solving the integral equation. The solutions of the integral equations are classified into (i) paramagnetic solution, (ii) spin glass with symmetric discrete distribution with more than three delta functions, (ii′) spin glass with symmetric distribution with more than three delta functions, (iii) discrete asymmetric ferromagnetic distribution, (iv) spin glass with symmetric continuous distribution, (v) asymmetric continuous distribution. The values of the concentration p of the +J bonds at which the solutions (ii) and (iii), (iv) and (v), (v) and (iii) are connected, are obtained to be p1=78, p2=0.869427 and p3=1112 respectively. It is expected that the symmetric spin glass, asymmetric continuous distribution, and discrete asymmetric distribution are realized in 12 ⩽p⩽p2, p2⩽p⩽p3 and p3⩽p⩽1, respectively. The distribution functions in each region are shown explicitly.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:157:y:1989:i:3:p:1195-1202

DOI: 10.1016/0378-4371(89)90039-3

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