Distribution of effective field in the ising spin glass of the +/- J model at T = O. Solutions as superpositions of delta-functions.
The integral equation for the distribution function of effective field of the +/- J random Ising model in the pair (Bethe) approximation is investigated. Its exact solutions at H (magnetic field) = O, T (temperature) = O and for z (coordination number) = 3 expressed as superpositions of 2N + 1 (more than 3), delta functions are considered. Then the integral equation is reduced to a system of algebraic equations of z - 1th degree with N + 1 unknowns. The system of the equations is solved by the Gröbner basis method with N = 1,2,3,4. The number of physically acceptable solutions for a given N is omega(N) + 1, where omega(N) is the number of divisors of N. The ground-state energy and entropy for these are calculated. They are very close in value (entropies are positive), and it is suggested that a number of physically acceptable solutions correspond to local stationary spin-glass states, as discussed in the literatures.
D055598:Chemical Phenomena; D002621:Chemistry; D005139:Eyeglasses; D008962:Models, Theoretical; D013816:Thermodynamics