Correlation at low temperature. I: Exponential decay

DOI10.1016/S0022-1236(03)00046-6zbMath1031.82003MaRDI QIDQ1410555

Jacob Schach Møller, Volker Bach

Publication date: 14 October 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

Gibbs measureexponential decay of correlationsWitten Laplacianlattice spin systems

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (12)

Localization at low temperature and infrared bounds ⋮ Clustering bounds on \(n\)-point correlations for unbounded spin systems ⋮ On Witten Laplacians and Brascamp-Lieb's inequality on manifolds with boundary ⋮ Epistemic democracy with correlated voters ⋮ Surface energy and boundary layers for a chain of atoms at low temperature ⋮ Gap universality of generalized Wigner and \(\beta\)-ensembles ⋮ Witten Laplacian method for the decay of correlations ⋮ Witten Laplacian method for generalized models of Kac type ⋮ A complete renormalization group trajectory between two fixed points ⋮ On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension ⋮ Sharp tunneling estimates for a double-well model in infinite dimension ⋮ Single scale cluster expansions with applications to many Boson and unbounded spin systems

Cites Work

• Supersymmetry and Morse theory
• Dobrushin uniqueness theorem and logarithmic Sobolev inequalities
• Remarks on decay of correlations and Witten Laplacians Brascamp-Lieb inequalities and semiclassical limit
• On the correlation for Kac-like models in the convex case
• Remarks on decay of correlations and Witten Laplacians. III: Application to logarithmic Sobolev inequalities
• Around a stationary phase theorem in large dimension
• Stochastic analysis on product manifolds: Dirichlet operators on differential forms
• Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature
• Low-temperature localisation for continuous spin-systems
• On Laplace integrals and transfer operators in large dimension: Examples in the nonconvex case
• REMARKS ON DECAY OF CORRELATIONS AND WITTEN LAPLACIANS II — ANALYSIS OF THE DEPENDENCE ON THE INTERACTION
• Metastability in stochastic dynamics of disordered mean-field models
• The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
• The low-temperature limit of transfer operators in fixed dimension
• On decay of correlations for unbounded spin systems with arbitrary boundary conditions
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