Information geometry of finite Ising models
2002; Elsevier BV; Volume: 47; Issue: 2-3 Linguagem: Inglês
10.1016/s0393-0440(02)00190-0
ISSN1879-1662
Autores Tópico(s)Markov Chains and Monte Carlo Methods
ResumoA model in statistical mechanics, characterised by a Gibbs measure, inherits a natural parameter-space geometry through an embedding into the space of square-integrable functions. This geometric structure reflects the underlying physics of the model in various ways. Here, we study the associated geometry and curvature for finite one- and two-dimensional Ising models as the lattice size N is varied. We show that there are temperature T and magnetic field h dependent critical values for the system size N∗(T,h) where the curvature varies rapidly and undergoes a change of sign. Such finite volume geometric transitions are necessarily continuous. By comparison with known indicators, we demonstrate that the criterion N≫N∗ provides a consistent constraint that lattice systems are qualitatively in their thermodynamic regime.
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