Communications in Mathematical Physics

, Volume 82, Issue 2, pp 261–304 | Cite as

Phase diagrams and cluster expansions for low temperature Open image in new window models

I. The phase diagram
  • John Z. Imbrie
Article

Abstract

Low temperature phase diagrams of two-dimensional
quantum field models are constructed. Let
lie in an (r−1)-dimensional space of perturbations of a polynomial withr degenerate minima. Perform a scaling
and assume λ«1. We constructk distinct states on\(\left( {\begin{array}{*{20}c} r \\ k \\ \end{array} } \right)\) hypersurfaces of codimensionk−1 in the space of perturbations. An expansion is used to exhibit exponential clustering of the Schwinger functions of each of these states. At the core of the construction is a general technique for finding the thermodynamically stable phases from a collection of competing minima. We draw on ideas of Pirogov and Sinai [24] for this problem.

Keywords

Neural Network Statistical Physic Phase Diagram Complex System Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • John Z. Imbrie
    • 1
  1. 1.Department of PhysicsHarvard UniversityCambridgeUSA

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