Ferromagnetic-spin glass transition in four-dimensional random-bond Ising model

Abstract

The four-dimensional +-J random-bond Ising model is studied using ground-state calculations. System sizes up to N=6^4 spins are considered. Here it is found that the ferromagnetic-spin glass transition occurs at a critical concentration p_c=0.28(1) of the antiferromagnetic bonds, which is comparable to values found previously by high-temperature series expansions. The transition is characterized by a correlation-length exponent \nu=1.0(1) and an order-parameter exponent \beta=0.4(1). Thus, this transition is in a different universality class from four-dimensional bond percolation, where \nu=0.678(50) and \beta=0.639(20).