Stochastic field effects in a two-state system: symmetry breaking and symmetry restoring

Abstract: We propose a theoretical model that incorporates both a time-varying stochastic field and thermal noise in a two-state system. In analyzing data from numerical simulations, we adopt a detailed microscopic approach that goes beyond the standard calculation of the order parameter. Specifically, we measure the probability distribution of the magnetization as a function of temperature and field strength, and compute the time required for the system to jump from one ordered state to the other. These measurements enable us to probe various ordered states in the system and investigate the symmetry breaking and symmetry restoring phenomena underlying the observed phase behavior.