Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. I: Cluster expansion
type: Item
instance of: scholarly article
title: Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. I: Cluster expansion
zbMATH Open document ID: 0663.60075
DOI: 10.1007/BF01225035
author: Yong Moon Park
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: This paper is the first part of an extension of the Pirogov-Sinai theory of phase transitions at low temperatures, applicable to lattice systems with finite range interactions, to infinite range interactions. Transforming the systems to a version of an interacting contour model, we develop a cluster expansion. Making appropriate assumptions about the interactions, we prove that for sufficiently low temperatures the expansion converges and the cluster property holds.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 4084706
zbMATH Keywords: Pirogov-Sinai theory of phase transitions
zbMATH Keywords: lattice systems with finite range interactions
zbMATH Keywords: cluster expansion
zbMATH Keywords: low temperatures
MaRDI profile type: Publication
cites work: First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory
cites work: Existence of a Phase Transition in Two-Dimensional and Three-Dimensional Ising Models
cites work: The pure phases (harmonic functions) of generalized processes or: Mathematical physics of phase transitions and symmetry breaking
cites work: Cluster expansion for abstract polymer models
cites work: The cluster expansion for classical and quantum lattice systems
cites work: Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. II: Phase diagram
cites work: On Ising's model of ferromagnetism
cites work: Q5564295
full work available at URL: https://doi.org/10.1007/bf01225035
OpenAlex ID: W2044818053
description: scientific article; zbMATH DE number 4084706