Ground State Properties of the ±<i>J</i>Ising Model in Two Dimensions

Abstract

We investigate the ground state properties of the ± J Ising model with asymmetric probability weight in two dimensions. We propose a numerical transfer matrix method which enables us to calculate directly the ground-state properties such as correlation functions, defect energy and entropy at T =0. We find that the spin glass correlation function decays in a power law like \(\tilde{g}(r)\sim{r}^{-\tilde{\eta}}\) with \(\tilde{\eta}\simeq0.21\) in the range \(0.5\leq{p}\lesssim0.85\), suggesting the weak universality of spin glass-the concentration of + J bond is denoted by p . At the ferromagnetic phase boundary locating around p =0.89, the ferromagnetic correlation function decays as \(g(r)\sim{r}^{-\tilde{\eta}}\) with η≃0.240±0.016, which suggests the weak universality of ferromagnetic critical exponent from the non-random critical point ( p =1, T =2.269···) to the ground sate counterpart. The behavior of correlation functions, and also that of defect energies indicate the existence of an extra-phase, called the random antiphase state, in \(0.85\lesssim{p}\lesssim0.89\).