Novel ballistic to diffusive crossover in the dynamics of a one dimensional Ising model with variable range of interaction

Abstract

The idea that the dynamics of a spin is determined by the size of its neighbouring domains was recently introduced (S. Biswas and P. Sen, Phys. Rev. E {\bf 80}, 027101 (2009)) in a Ising spin model (henceforth, referred to as model I). A parameter $p$ is now defined to modify the dynamics such that a spin can sense domain sizes up to $R=pL/2$ in a one dimensional system of size $L$. For the cutoff factor $p$ \to 0$,thedynamicsisIsinglikeandthedomainsgrowwithtime$t$diffusivelyas$ t^{1/z}$with$z=2$,whilefor$p=1$,theoriginalmodelIshowedballisticdynamicswith$z \simeq 1$.Forintermediatevaluesof$p$,thedomaingrowth,magnetisationandpersistenceshowmodelIlikebehaviouruptoamacroscopiccrossovertime$ t_1 \sim pL/2$.Beyond$t_1$,characteristicpowerlawvariationsofthedynamicquantitiesarenolongerobserved.Thetotaltimetoreachequilibriumisfoundtobe$t = apL + b(1-p)^3L^2$,fromwhichweconcludethatthelatertimebehaviourisdiffusive.Wealsoconsiderthecasewhenarandombutquenchedvalueof$p$ is used for each spin for which ballistic behaviour is once again obtained.

14 pages, 12 figures. Published version of Journal of Physics A

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Cited by in corpus (4)

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• Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation
• Effect of the nature of randomness on quenching dynamics of Ising model on complex networks
• Opinion dynamics model with domain size dependent dynamics: novel features and new universality class