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

Abstract

Free energy as a function of polarization is calculated for the square-lattice J_1J1-J_2J2 Ising model for J_2 < |J_1|/2J2<|J1|/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|/4J2>|J1|/4. These findings enrich our knowledge of the J_1J1-J_2J2 Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.