On the critical temperature of the two-dimensional Ising spin glass

Abstract

The critical temperature of any two-dimensional Ising model can in principle be determined exactly, providing there is a finite unit cell. This property is used to investigate the dependence of the critical temperature on the size of the unit cell where the exchange coupling between spins in the unit cell are assigned from a Gaussian distribution. It is found that as the number of spins in the unit cell is increased the critical temperature falls. Extrapolation to infinite unit cell, which corresponds to a spin glass, indicates that the critical temperature vanishes.