Higher-order tensor renormalization group study of the J1-J2 Ising model on a square lattice

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.

Automated summary

The phase transitions of the J(1) - J(2) Ising model on a square lattice were studied using the higher-order tensor renormalization group method. The results indicate that the region of the first-order transition is slightly narrower than in previous studies and the region where the critical exponent changes does not necessarily coincide with the Ashkin-Teller region.