Thursday, January 31, 2019

Describe Ising model dynamics in stochastic differential equation or stochastic process


The Ising model is described by the Hamiltonian $$ H(\sigma) = - \sum_{} J_{ij} \sigma_i \sigma_j -\mu \sum_{j} h_j\sigma_j, $$ and is treated extensively by equilibrium statistical mechanics. Consider a Ising model at equilibrium is affected by a sudden change in external parameters such as the temperature and the external field and the system goes to a new equilibrium state after some time. Monte Carlo simulation can simulate this non-equilibrium process, but can this relaxation from a non-equilibrium state to a equilibrium state be described by a system of coupled differential equation or a stochastic process?




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