Domain-wall renormalization-group study of the random Heisenberg model

Abstract

The random Heisenberg model with a Gaussian distribution of nearest-neighbor interactions is studied for the pure spin-glass case where the average interaction vanishes. The distribution of domain-wall energies at zero temperature is calculated using a spin-quench algorithm to find the ground-state energy for finite lattices. A renormalization-group transformation is set up which preserves the domain-wall energy distribution when the lattice parameter is changed. In the strong-coupling regime (zero temperature) the model iterates toward weak coupling and therefore exhibits a ‘‘phase transition at zero temperature’’ in both two and three dimensions. The correlation-length exponent is ν=0.714±0.015 in two dimensions and ν=1.54±0.19 in three dimensions. The lower critical dimension is four.