Higher-order tensor renormalization group study of the J_{1}-J_{2} Ising model on a square lattice.

Abstract

Phase transitions of the J_{1}-J_{2} Ising model on a square lattice are studied using the higher-order tensor renormalization group (HOTRG) method. This system involves a competition between the ferromagnetic interaction J_{1} and antiferromagnetic interaction J_{2}, and in previous studies, weak first-order and second-order transitions were observed near the ratio g=J_{2}/|J_{1}|=1/2. It has also been suggested that the universality class of the second-order phase transition connected to the first-order transition line for g>1/2 belongs to the Ashkin-Teller class, which is characterized by a continuously varying critical exponent with g, as predicted by field-theoretical and other studies. Our results, based on the HOTRG calculations for significantly larger sizes, indicate that the region of the first-order transition is marginally narrower than that in previous studies. Furthermore, it is suggested that the region where the critical exponent changes does not necessarily coincide with the Ashkin-Teller region.