Rigorous upper and lower bounds on the critical temperature in Ising models with random, quenched, broken-bond disorder

Abstract

Upper and lower bounds for T_c(p) are rigorously established for the Ising model with random, quenched, broken-bond disorder. T_c is the critical temperature, defined by the onset of a non-zero spontaneous magnetization, and p is the fraction of unbroken bonds. Bounds are also found for other quantities, such as the two-point correlation functions. These bounds may be applied at any temperature and any value of p with 0c and p_c is the lowest value of p above which the system has a non-zero spontaneous magnetization at T=O.