Phase Transition in an Ising Model near the Percolation Threshold

Abstract

The phase transition near the percolation threshold in an Ising model with random exchange is investigated. The mean-field theory of the transition is discussed. The cross-over exponent $\varphi$ and susceptibility are caluclated in $6-\epsilon$ dimensions using renormalization-group methods with the result $\varphi =1+O\left({\epsilon }^3\right)$. $\varphi$ is also shown to be 1 near one dimension.