Cluster mean field analysis of spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices

This paper studies totally asymmetric simple exclusion processes (TASEPs) on two intersected lattices. There are four types of particles in the model, and the particles have pre-defined destinations. Spontaneous symmetry breaking (SSB) phenomenon exists in the model. When parameter γ < 1 , simple mean field analysis fails to describe the four kinds of particles due to neglect of correlation of sites. In this paper, we carry out a cluster mean field analysis for the asymmetric phase boundaries and density profiles, the correlation of three sites is considered in the analysis. It is found that analytical results are in good agreement with Monte Carlo simulation ones. When γ = 1 , the simple mean field analysis can be adopted in the analysis, and the cluster mean field analytical results are closer to the simulation ones than that of simple mean field analysis.