Phase Transition of Ising Spin Glass Models in Two Dimensions

Abstract

We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy $\overline{Δ F(T)} and the Binder parameter g_L, on finite L × L (L ≤ 24) lattices at very low temperatures T. We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution, $\overline{Δ F(T)} at very low temperatures slightly increases with L and g_L intersect at T ∼ 0.25J. These results suggest a non-zero temperature phase transition, T_c ≠ 0. On the other hand, for the Gaussian distribution, $\overline{Δ F(T)} decreases as L increases even at T = 0 and g_L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T_c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J.