Fermions and loops on graphs: I. Loop calculus for determinants

DOI10.1088/1742-5468/2008/12/P12011zbMath1456.82038MaRDI QIDQ5239457

Michael Chertkov, Vladimir Y. Chernyak

Publication date: 22 October 2019

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

zbMATH Keywords

gauge theoriesmessage-passing algorithmsrigorous results in statistical mechanics

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Analysis on supermanifolds or graded manifolds (58C50)

Related Items (2)

Fermions and loops on graphs: II. A monomer–dimer model as a series of determinants ⋮ Gauges, loops, and polynomials for partition functions of graphical models

Uses Software

• GMRFLib

Cites Work

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• Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology
• Belief propagation and loop series on planar graphs
• Loop calculus in statistical physics and information science
• Loop series for discrete statistical models on graphs
• Modern Coding Theory
• Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms
• An analysis of belief propagation on the turbo decoding graph with Gaussian densities
• Gaussian Markov Random Fields
• Tree-based reparameterization framework for analysis of sum-product and related algorithms
• Fermions and loops on graphs: II. A monomer–dimer model as a series of determinants
• Statistical theory of superlattices
• On Ising's model of ferromagnetism

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