Critical exponents at the Nishimori point

Abstract

The Nishimori point of the random bond Ising model is a prototype of renormalization group fixed points with strong disorder. We show that the exact correlation length and crossover critical exponents at this point can be identified in two and three spatial dimensions starting from properties of the Nishimori line. These are the first exact exponents for frustrated random magnets, a circumstance to be also contrasted with the fact that the exact exponents of the Ising model without disorder are not known in three dimensions. Our considerations extend to higher dimensions and models other than Ising.

Figures (1)

• Figure 1: Phase diagram of the $\pm J$ random bond Ising model. The Nishimori line (dashed) crosses the ferromagnetic phase boundary at the Nishimori multicritical point (dot). In two dimensions the spin glass phase is not observed for $T>0$.