Interfacial approach tod-dimensional �J Ising models in the neighborhood of the ferromagnetic phase boundary

Abstract

Two- and three-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase (FP) boundary in the concentration-temperature (p-T) plane are studied, investigating the size dependence of interfacial free energies calculated by a transfer matrix method. Thep andT dependences of two stiffness exponents relevant to the FP and the nonferromagnetic ordered phase lead to the following results in two dimensions, giving a unified view. It is confirmed that the random antiphase state (RAS) exists in contact with the vertical FP boundary. Spatial fluctuations are dominant near the vertical boundary, which is separated by the Nishimori line from the remaining FP boundary governed by thermal fluctuations. The RAS is a kind of Mattis spin glass such that it changes to the FP smoothly with nonsingular physical connectivity, but with a percolation singularity of its ferromagnetic part. Universal finite-size critical amplitudes are consistent with them. Results in three dimensions give only suggestions which are similar to the two-dimensional results. These results suggest important insight into spin-glass properties in higher dimensions.