Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model

TL;DR

This study investigates the free energy landscape and metastable states of the square-lattice J1-J2 Ising model using RLFA and Monte Carlo simulations, revealing complex phase transitions and metastable configurations.

Contribution

It introduces a detailed analysis of metastable states and phase transitions in the J1-J2 Ising model using RLFA and MC, highlighting phenomena not captured by mean field theory.

Findings

Identification of metastable states with various polarizations

Discovery of slab-droplet phase transitions at low temperature

Additional slab-droplet transitions for J2 > |J1|/4

Abstract

Free energy as a function of polarization is calculated for the square-lattice $J_1$-$J_2$ Ising model for $J_2 < |J_1|/2$ using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at $J_2 > |J_1|/4$. These findings enrich our knowledge of the $J_1$-$J_2$ Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.