Information geometry of finite Ising models

✍ Scribed by Dorje C. Brody; Adam Ritz

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 152 KB
• Volume: 47
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00190-0

✦ Synopsis

A model in statistical mechanics, characterised by a Gibbs measure, inherits a natural parameterspace 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.