Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm

Abstract

We developed a genetic algorithm (GA) in the Heisenberg model that combines a triadic crossover and a parameter-free genetic algorithm. Using the algorithm, we examined the ground-state stiffness of the $\pm J$ Heisenberg model in three dimensions up to a moderate size range. Results showed the stiffness constant of $\theta = 0$ in the periodic-antiperiodic boundary condition method and that of $\theta \sim 0.62$ in the open-boundary-twist method. We considered the origin of the difference in $\theta$ between the two methods and suggested that both results show the same thing: the ground state of the open system is stable against a weak perturbation.