An extended chain Ising model and its Glauber dynamics

Abstract

It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model, single spin double-well potentials and a pure phonon heat bath of a specific energy exchange with the spins. The extension method is easy to apply to high dimensional cases. Then the single spin-flip probability (rate) of the ECI model is deduced based on the Boltzmann principle and general statistical principles of independent events and the model is simplified to an extended chain Glauber—Ising (ECGI) model. Moreover, the relaxation dynamics of the ECGI model were simulated by the Monte Carlo method and a comparison with the predictions of the special chain Glauber—Ising (SCGI) model was presented. It was found that the results of the two models are consistent with each other when the Ising chain length is large enough and temperature is relative low, which is the most valuable case of the model applications. These show that the ECI model will provide a firm physical base for the widely used single spin-flip rate proposed by Glauber and a possible route to obtain the single spin-flip rate of other form and even the multi-spin-flip rate.