Low-temperature properties of the±JIsing spin glass in two dimensions

The replica Monte Carlo simulation method and finite-size transfer-matrix method are used to study low-temperature properties of the $\pm J$ Ising spin glass in two dimensions. We find the spin-glass susceptibility exponent $\gamma =5.11\mathrm{}\pm 0.05$ with a zero-temperature transition. The ground-state entropy $s_0=0.071\mathrm{}\pm 0.007$ by Monte Carlo simulation agrees well with previous transfer-matrix calculation, and the specific heat at low temperature has an asymptotic form $\frac{c}{k_B}\approx \frac{1.3J^2}{{\left(k_{B}T\right)}^2}{e}^{\frac{-2J}{\left(k_{B}T\right)}}$, which indicates an energy $2J$ as low-lying excitations. We show that the replica Monte Carlo method is much faster than standard annealing for finding ground states.