Explanation of the freezing temperature in spin glasses

Abstract

The freezing of spins in the two‐dimensional ±J‐model [1,2] (anti‐ and ferromagnetic nearest neighbour bonds between Ising spins) is investigated for the case of a one‐spin‐flip‐dynamic (as used in Monte‐Carlo calculations). The phenomenon is caused by the existence of finite energy barriers between the different ground‐state valleys. The barrier heights are calculated by a numerical method turning one ground state to its inverse. The freezing temperature is determined by the vanishing of the free energy barriers between the valleys. The corresponding entropy is calculated by the Transfermatrix‐Method. The free energy barriers vanish at Tf≂1.3±0.1 in good agreement with the cusp of the susceptibility in Monte‐Carlo calculations. The long‐time behaviour of spin glasses is governed by the mentioned free energy barriers.