Nonlinear dynamics for the Ising model
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann's model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a nonlinear counterpart of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. We provide sharp quantitative convergence analysis at high temperatures for this model. Our analysis combines tools such as information percolation, a novel coupling of the Ising model with inhomogeneous Erdős-Rényi random graphs, and a fragmentation process augmented by branching processes. Joint work with Alistair Sinclair.
Area: CS28 - Statistical mechanics and interacting particle systems (Elisabetta Candellero)
Keywords: Ising model; Nonlinear dynamics; Branching process; Mixing time.
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