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 \ ildeg(r)∼r−\ ildeη with \ ildeη\simeq0.21 in the range 0.5≤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)∼r−\ ildeη with η\simeq0.240±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\lesssimp\lesssim0.89.
