Ising spin glass models versus Ising models: an effective mapping at high temperature: I. General result

DOI10.1088/1742-5468/2006/10/P10004zbMath1456.82525arXivcond-mat/0607498MaRDI QIDQ4968892

Massimo Ostilli

Publication date: 9 July 2019

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

Full work available at URL: https://arxiv.org/abs/cond-mat/0607498

zbMATH Keywords

networksrandom graphsseries expansionsdisordered systems (theory)phase diagrams (theory)

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items (4)

Mean field dilute ferromagnet: High temperature and zero temperature behavior ⋮ Ising spin glass models versus Ising models: an effective mapping at high temperature: II. Applications to graphs and networks ⋮ Ising spin glass models versus Ising models: an effective mapping at high temperature: III. Rigorous formulation and detailed proof for general graphs ⋮ On forest expansions for two-body partition functions on tree-like interaction graphs

Cites Work

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• Broken replica symmetry bounds in the mean field spin glass model
• The Parisi formula
• Random-energy model: An exactly solvable model of disordered systems
• Equilibrium and off-equilibrium simulations of the Gaussian spin glass
• Low-temperature phase of the Ising spin glass on a hypercubic lattice
• Loops of any size and Hamilton cycles in random scale-free networks
• Generalizations of the Weiss Molecular Field Theory of Antiferromagnetism
• Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

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