General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
type: Item
instance of: scholarly article
title: General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
zbMATH Open document ID: 1073.82012
author: José A. Cuesta
author: Ángel Sánchez
published in: Journal of Statistical Physics
publication date: 2004-08-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/cond-mat/0306354
review text: The authors undertake the critique of a famous general statement, namely there cannot be phase transitions in one-dimensional systems with short range interactions. To carry out this program, they proceed along two complementary directions. First, they review the existing results about nonexistence of phase transitions in short-ranged one-dimensional systems. The authors note that the well-known argument by Landau about domain walls is heuristic and relies on approximate calculations; they also comment briefly on this. Next, the authors discuss several one-dimensional models proposed in the past which exhibit true thermodynamic phase transitions. Having thus established clearly the existence of phase transitions in one-dimensional systems with short range interactions, they move their second contribution, introducing rigorously a very general theorem on the impossibility of phase transitions in such models. The authors also show how models not fulfilling one of the hypothesis exist which do have phase transitions and comment on the ways to violate those hypotheses.
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 47N55
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B23
zbMATH DE Number: 2085873
zbMATH Keywords: phase transitions
zbMATH Keywords: one-dimensional systems
zbMATH Keywords: short-range interactions
zbMATH Keywords: transfer operators
zbMATH Keywords: rigorous results
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
arXiv ID: cond-mat/0306354
OpenAlex ID: W3104923947
DOI: 10.1023/B:JOSS.0000022373.63640.4E
Recommended article: Erratum to: General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
Recommended article: Absence of phase transitions in certain one-dimensional long-range random systems
Recommended article: Existence result for the one-dimensional full model of phase transitions
Recommended article: Phase transitions in one-dimensional translation invariant systems: a Ruelle operator approach
Recommended article: On a phase transition in a one-dimensional non-homogeneous model
Recommended article: Q3325363
Recommended article: Q3776360
Recommended article: On the absence of phase transition in continuous one-dimensional Gibbs systems with no hard core
Recommended article: Absence of phase transitions for continuum models of dimension d&gt;1
Recommended article: Existence of Dynamic Phase Transitions in a One-Dimensional Lattice Model with Piecewise Quadratic Interaction Potential
description: scientific article