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The random walk representation of classical spin systems and correlation inequalities

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1982Publisher:Springer Science and Business Media LLCJournal:Communications in Mathematical Physics, volume 83, pages 123-150 (issn: 0010-3616, eissn: 1432-0916,

Authors: Brydges, David; Fröhlich, Jürg; Spencer, Thomas;

doi: 10.1007/bf01947075

The random walk representation of classical spin systems and correlation inequalities

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Abstract

Ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion. By using a mixed spinrandom walk representation we present a unified approach to many recently established correlation inequalities. As an application of these inequalities we obtain a simple proof of the mass gap for the λ(φ4)2 quantum field model. We also establish new upper bounds on critical temperatures.

Related Organizations

DePaul University
United States
Courant Institute of Mathematical Sciences
United States
New York University
United States
Institut des Hautes Études Scientifiques
France

Keywords

82A67, 81E10

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