Critical exponents of the binomial Ising Spin Glass in dimension four; non-universality

Abstract

Extensive simulations are made on the bimodal Ising Spin Glass (ISG) in dimension four. The transition temperature is established using a combination of standard finite size scaling and of thermodynamic derivative peak data. Measurements in the thermodynamic limit regime are analysed so as to estimate critical exponents and confluent correction terms. Comparisons with results on other 4d ISGs show that the susceptibility and correlation length critical exponents $\gamma$ and $\nu$ depend on the form of the interaction distribution. From this observation it can be deduced that critical exponents are not universal in ISGs.