The ordering temperature and critical exponents of the binomial Ising spin glass in dimension three

Abstract

We compare numerical estimates from different sources for the ordering temperature $T_g$ and the critical exponents of the Ising spin glass in dimension three with binomial ($\pm J$) interactions. Corrections to finite size scaling turn out to be important especially for parameters such as the Binder cumulant. For non-equilibrium parameters it is easier to approach the large size limit and to allow for corrections to scaling. Relying principally on such data, a crossing point defines the freezing temperature $T_g$; the possibility that the ordering temperature is zero can definitively be excluded. We estimate an ordering temperature $T_g = 1.195(15)$, with associated estimates of the critical exponents for which corrections to finite size scaling are well under control. Among the parameters evaluated is the leading dynamic correction to scaling exponent $w$.