The Simplest Nearest-Neighbour Spin Systems on Regular Graphs: Time Dynamics of the Mean Coverage Function
2002, v.8, Issue 3, 527-546
We establish a characterization of the class of the simplest nearest neighbour spin systems possessing the mean coverage function (mcf) that obeys a second order differential equation, and derive explicit expressions for the mcf's of the above models. Based on these expressions, the problem of ergodicity of the models is studied and bounds for their spectral gaps are obtained.
Keywords: interacting spin systems,mean coveragefunction,voter models,ergodicity,spectral gap