Information geometry of finite Ising models

DOI10.1016/S0393-0440(02)00190-0zbMath1021.37005OpenAlexW2004101805WikidataQ125630511 ScholiaQ125630511MaRDI QIDQ1400163

Dorje C. Brody, Adam Ritz

Publication date: 13 August 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0393-0440(02)00190-0

zbMATH Keywords

phase transitionsIsing modelsstatistical mechanicsinformation geometrylattice systemsFisher-Rao metricsquare-integrable functionsRicci scalar curvature

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Dynamical aspects of statistical mechanics (37A60)

Related Items (10)

Quantum lattice model with local multi-well potentials: Riemannian geometric interpretation for the phase transitions in ferroelectric crystals ⋮ Towards an information geometric characterization/classification of complex systems. I: Use of generalized entropies ⋮ Thermodynamic geometry of Ising ferromagnet in an external magnetic field: a self-consistent field theory calculation ⋮ Information geometric methods for complexity ⋮ Weyl geometric approach to the gradient-flow equations in information geometry ⋮ Monotonicity of the scalar curvature of the quantum exponential family for transverse-field Ising chains ⋮ Phase transition and thermodynamic stability in extended phase space and charged Hořava-Lifshitz black holes ⋮ From Complexity to Information Geometry and Beyond ⋮ Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction–diffusion model ⋮ Thermodynamic geometry of Kaniadakis statistics

Cites Work

• Geometrical structure of the state space in classical statistical and phenomenological thermodynamics
• Informative geometry of probability spaces
• On the Riemannian metrical structure in the classical statistical equilibrium thermodynamics
• Information geometry in functional spaces of classical and quantum finite statistical systems
• The geometry of asymptotic inference. With comments and a rejoinder by the author
• Statistical geometry in quantum mechanics
• Geometrization of statistical mechanics
• Riemannian geometry and stability of thermodynamical equilibrium systems
• Consistency of microcanonical and canonical finite-size scaling
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