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We calculate the (restricted) free energy as a function of polarization forthe square-lattice J1-J2 Ising model using the Random local field approximation(RLFA) and Monte Carlo (MC) simulations. Here we consider mainly couplingconstants in the range 0 < J2 < 1/2 at J1 = - 1, for which the ground state isferromagnetic (or N{\'e}el antiferromagnetic when J1 = 1). Within RLFA, ametastable state with zero polarization is present in the ordered phase, whichwas recently discussed by V.A. Abalmasov and B.E. Vugmeister, Phys. Rev. E 107,034124 (2023). In addition, the free energy calculated within RLFA indicates ageometric slab-droplet phase transition at low temperature, which cannot bedetected in the mean field approximation. In turn, exact calculations of thefree energy for the sample size L = 6 and MC simulations for L = 10 revealmetastable states with a wide range of polarization values in the orderedphase, the origin of which we discuss. The calculations also reveal additionalslab-droplet transitions (at J2 > 0.25). These findings enrich our knowledge ofthe J1-J2 Ising model and the RLFA as a useful theoretical tool to study phasetransitions in spin systems.

Free energy and metastable states in the square-lattice J1-J2 Ising model