Accurate ground-state entropies from population Monte Carlo: The antiferromagnetic Ising model on the Shastry-Sutherland lattice

Abstract

We demonstrate how the population annealing Monte Carlo simulation method can be used to compute the ground-state entropy to high precision. This approach is tested for the classical antiferromagnetic Ising model on the Shastry-Sutherland lattice with diagonal couplings chosen twice as strong as the nearest-neighbor interactions. In the absence of an external magnetic field, the model is known to be disordered at all temperatures, with a macroscopically degenerate ground state. We find the ground-state entropy to be $0.458\,777\,78(10)$ per site, which is in good agreement with the estimate of a recent study using the corner transfer matrix renormalization group method. The sampled ground-state configurations are analyzed by considering the bond configurations, the local-energy configurations, and the spin-spin correlations. While all observations are consistent with the disordered nature of the ground state, the numerical data suggest a power-law decay of the size distribution of clusters of sites with local energies different from the ground-state level.