Identification of Metastable States in Finite Temperature Simulations: A Self-Organization Approach

In mean-field approximations, metastable states are often represented as saddle points of self-consistent equations. There seems, however, no established procedure to identify metastable states in simulation data at finite temperatures. Here we propose a method based on a finite mixture model. 1) In the proposed method, we fit a mixture P (y) = ∑ c wc · Pc(y|λc) of the distributions {Pc} to a given set of data and regard each component Pc as a metastable state. The parameters {λc} and weights {wc} (c wc=1) of the components are estimated from the data by EM algorithm, which gives maximum likelihood estimates (MLE) of these parameters. In this algorithm, no auxiliary assumption for the assignment of each sample to the components is required. The classification of the data is automatically determined by the algorithm, once we give the number cmax of the component distributions. In this paper, we apply this method to the analysis of binary patterns {{dji}} generated by the simulations of Ising spin glass models. Here and hereafter a suffix i is the index of a sample, while a suffix j is the index of an element in a sample (e.g., the site of a spin). Our model is expressed as