Critical thermodynamics of the two-dimensional +/-J Ising spin glass

TL;DR

This paper analyzes the thermodynamic properties of the 2D +/-J Ising spin glass, revealing an effective energy gap and a growing length scale at low temperatures, based on exact partition function calculations.

Contribution

It provides an exact computation of the partition function for 2D +/-J Ising spin glasses and uncovers the effective gap and scaling behavior of low-temperature excitations.

Findings

Low temperature specific heat scales as exp(-2J/T)

Effective energy gap is 2J despite a ground state gap of 4J

Cross-over length scale grows as exp(J/T)

Abstract

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an ``effective'' gap of size 2J; in addition, an associated cross-over length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low-lying excitations and by the way low energy domain walls proliferate in this model.