Thermodynamic equilibrium of ±J Ising model on square lattice

Abstract

We constructed a theoretical magnetic phase diagram in an external magnetic field $T\left(P_{+}\right)$, making it possible to determine the conditions for the existence of ferromagnets, antiferromagnets, and spin glass phases. The high-performance CUDA software package was used to the complete enumeration of all configurations of finite number spins in the $\pm J$ Ising model. We performed the rigorous numerical calculation of the partition function of $N=8\times 8$ systems of interacting spins with open boundary conditions. We used Monte Carlo methods like the Metropolis algorithm to calculate the critical temperatures for $N=40\times 40$ spins. The results of the Monte Carlo experiments are consistent with rigorous calculation data. The transition from the spin glass to the induced ferromagnetic state in an external field occurs without any critical change in the heat capacity. We used the $\pm J$ Ising model to calculate the instability line ($AT$—line) for the heat capacity of spin glass in the $H-T$ diagram in an external magnetic field and the behavior of magnetic susceptibility in an external magnetic field. A rigorous calculation of the partition function allowed us to calculate all possible states and their thermodynamic probability. The calculation of the partition function meant that the model’s physics was obtained in an equilibrium state. The instability line was calculated for spin glass in the equilibrium state.