Low-temperature states of the Ising ±J model on a square lattice

Abstract

Using the complete enumeration method, we accurately calculated all possible states of the Edwards–Anderson model on a simple square lattice of 8 × 8 spins. The ground state energies of the studied finite-size samples were determined. The macroscopic degeneracy of the ground state in frustrated spin systems arises from the combinatorics of frustrated plaquettes, i.e., the number of ways to place frustrated spin pairs on the lattice. The algorithm for calculating energy, spin excess, and ground state configurations is based on identifying the arrangement of frustrations. The dependence of the ground state spin excess in the Edwards–Anderson model on an external magnetic field has a discrete (step-like, stair-like) character. Critical values of the external magnetic field, at which large peaks in residual entropy occur, were calculated. The nature of these large entropy peaks is explained by the fact that, at certain critical values of the external magnetic field, the sum of several spin configurations with different interaction energies and Zeeman energies, i.e., with different values of spin excess, will have the same total energy. The degeneracy multiplicities of states with the same total energy are summed up at the critical magnetic field value. The areas of existence of low-temperature states have been determined.