Some Critical Properties of the Eight-Vertex Model

Abstract

The eight-vertex model solved by Baxter is shown to be equivalent to two Ising models with nearest-neighbor coupling interacting with one another via a four-spin coupling term. The critical properties of the model in the weak-coupling limit are in agreement with the scaling hypothesis. In this limit where $\ensuremath{\alpha}\ensuremath{\rightarrow}0$, the critical indices obey $\frac{\ensuremath{\gamma}}{{\ensuremath{\gamma}}_{0}}=\frac{\ensuremath{\beta}}{{\ensuremath{\beta}}_{0}}=\frac{\ensuremath{\nu}}{{\ensuremath{\nu}}_{0}}=1\ensuremath{-}\frac{1}{2}\ensuremath{\alpha}$, $\frac{\ensuremath{\delta}}{{\ensuremath{\delta}}_{0}}=\frac{\ensuremath{\eta}}{{\ensuremath{\eta}}_{0}}=1$, with the subscripts zero denoting the index values for the ordinary two-dimensional Ising model.