Theoretical methods in the critical region of a phase transition

秀稔 西森, Hidetoshi Nishimori, Gerardo Ortíz

Murtazaev Akai Kurbanovich, Ibaev Zhavrail Gadzhievich

The anisotropic Ising model with competing interactions in the region of transition from a modulated phase into paramagnetic state is investigated by the Monte-Carlo methods. By means of histogram analysis and the finite-size scaling method, the modulated – paramagnetic phase transition is shown to be a second order phase transition. Critical parameters and temperatures of phase transitions in this region are calculated.

Akai Kurbanovich Murtazaev, Zhavrail G. Ibaev

Abstract Monte Carlo methods are used to study the anisotropic Ising model with competing interactions in the region of the phase transition from the modulated to the paramagnetic phase. Using histogram analysis of Monte Carlo data and the theory of finite-size scaling, it is shown that the transition from the modulated state to the paramagnetic one is a second-order phase transition. The critical parameters and temperatures of phase transitions in this region are calculated. It is shown that the modulated–paramagnetic phase transition cannot be described within the framework of the known universality classes of critical behavior.

John F. Nagle

Kota Yoshiyama, Koji Hukushima

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.

David A. Lavis, Roman Frigg