The Information Geometry of the Spherical Model

Abstract

Motivated by previous observations that geometrizing statistical mechanics offers an interesting alternative to more standard approaches,we have recently calculated the curvature (the fundamental object in this approach) of the information geometry metric for the Ising model on an ensemble of planar random graphs. The standard critical exponents for this model are alpha=-1, beta=1/2, gamma=2 and we found that the scalar curvature, R, behaves as epsilon^(-2),where epsilon = beta_c - beta is the distance from criticality. This contrasts with the naively expected R ~ epsilon^(-3) and the apparent discrepancy was traced back to the effect of a negative alpha on the scaling of R. Oddly,the set of standard critical exponents is shared with the 3D spherical model. In this paper we calculate the scaling behaviour of R for the 3D spherical model, again finding that R ~ epsilon^(-2), coinciding with the scaling behaviour of the Ising model on planar random graphs. We also discuss briefly the scaling of R in higher dimensions, where mean-field behaviour sets in.

7 pages, no figures

References in corpus (2)

• The Information Geometry of the One-Dimensional Potts Model
• The Information Geometry of the Ising Model on Planar Random Graphs

Cited by in corpus (24)

• Quantum enhanced measurements without entanglement
• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Thermodynamic curvature measures interactions
• Thermodynamic curvature and black holes
• Information Geometry and Phase Transitions
• Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
• Information geometric methods for complexity
• On Grover's Search Algorithm from a Quantum Information Geometry Viewpoint
• Information geometry in quantum field theory: lessons from simple examples
• Thermodynamics and Thermodynamic geometry of Park black hole
• Geometrothermodynamics of the Kehagias-Sfetsos Black Hole
• Information Geometry on the Space of Equilibrium States of Black Holes in Higher Derivative Theories
• Thermodynamic geometry of a kagome Ising model in a magnetic field
• Geometrical aspects of a generalized statistical mechanics
• Geometrothermodynamics in Horava-Lifshitz gravity
• On the monotonicity of scalar curvature in classical and quantum information geometry
• A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time
• Thermodynamic geometry of pure Lovelock black holes
• Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes
• Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models
• Physical and thermodynamic properties of quartic quasitopological black holes and rotating black branes with nonlinear source
• $\mu PT$ statistical ensemble: systems with fluctuating energy, particle number, and volume
• Phase boundaries and the Widom line from the Ruppeiner geometry of fluids
• Nonperturbative thermodynamic extrinsic curvature of the anyon gas