On multi-spin flip critical dynamics of one-dimensional Ising models

Nobuyasu Ito, Tetsuhiko Chikyu

Michel Droz, J. Kamphorst Leal da Silva, Anna‐Sapfo Malaspinas

Eduardo Lage

Recent results concerning non-universality in the dynamical critical behavior of the one-dimensional Ising model, are generalised to several formulations of the Potts model, using arguments based on domain wall motion. By applying real-space renormalisation group methods, the authors also study the dynamical Ising model, with single flips, both for a period distribution of nearest-neighbor exchanges and for the random chain (with nonzero couplings). They show that the critical dynamical exponent is z=1+J M /J m where J M (J m ) is the greatest (smallest) of the exchanges.

C K Harris

Investigates the bicritical dynamics of one-dimensional bond-diluted kinetic Ising models in the percolation limit at criticality. A wide class of single-spin-flip dynamics is applied and domain boundary diffusion arguments are used to identify the dominant processes producing flipping of the ordered finite chain segments constituting the diluted chain. Exact expressions for the rate of flip as a function of length of segment are obtained and are used to derive corresponding expressions for the decay of equilibrium correlations, and of the magnetisation (from a non-equilibrium uniformly magnetised initial state) in the chain. The results are in agreement with those of earlier rigorous calculations restricted to the special case of Glauber dynamics.

Dong J. Lee, Cheol-Ju Kim, Jong‐Myung Lee

赵兴宇, 黄心茹, 樊小辉 +1 more

It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model,single spin doublewell 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.