The Curie-Weiss model -- an approach using moments
Werner Kirsch
TL;DR
This paper establishes probabilistic limit theorems for the Curie-Weiss model of magnetism using elementary moment-based methods, providing a rigorous mathematical foundation for understanding its large-scale behavior.
Contribution
It introduces a straightforward moment method approach to prove laws of large numbers and limit theorems for the Curie-Weiss model, simplifying previous proofs.
Findings
Proved laws of large numbers for the model
Established central and non-central limit theorems
Provided elementary proofs based on moments
Abstract
We prove laws of large numbers as well as central and non-central limit theorems for the Curie-Weiss model of magnetism. The rather elementary proofs are based on the method of moments.
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Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods