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Possibility of high-temperature phase transitions due to the many-particle nature of the potential

Possibility of high-temperature phase transitions due to the many-particle nature of the potential POSSIBILITY OF HIGH-TEMPERATURE PHASE TRANSITIONS DUE TO THE MANY-PARTICLE NATURE OF THE POTENTIAL R. L. Dobrushin and M. R. Martirosyan Small nonfinite perturbations of a Gibbs random field are considered. It is shown that if certain natural conditions on the rate of decrease of the perturbing potential at arbitrarily high temperatures are violated then the free energy may cease to be analytic. I. We consider a set q~ of translationally invariant (in general, complex-valued) potentials U={UA(z~), A6~(Z~), xA~X~}, (1.1) where ~ is a v-dimensional integral lattice, ~(Z ~) is the set of all finite subsets of Z~, X is some finite set of states of a particle, and X A is the set of configurations xA=(xt; xt6X, t~A). We consider the partition function (with "empty boundary conditions") ZA(U)-~- Z exp{--Hu(xA)}, U6@~, A6~(Zv), (1.2) xAEX A where the Hamiltonian is H~ (xA) 2~ UA (xA), xA E X A (1.3) AcA (here and in what follows, x A is the restriction of the configuration x A to the set A~A). One of the criteria generally adopted in statistical mechanics for the absence of phase transitions for some real-valued potential ~ is the requirement of nonvanishing of the partition function ZA(U http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theoretical and Mathematical Physics Springer Journals

Possibility of high-temperature phase transitions due to the many-particle nature of the potential

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References (3)

Publisher
Springer Journals
Copyright
1988 Plenum Publishing Corporation
ISSN
0040-5779
eISSN
1573-9333
DOI
10.1007/BF01017482
Publisher site
See Article on Publisher Site

Abstract

POSSIBILITY OF HIGH-TEMPERATURE PHASE TRANSITIONS DUE TO THE MANY-PARTICLE NATURE OF THE POTENTIAL R. L. Dobrushin and M. R. Martirosyan Small nonfinite perturbations of a Gibbs random field are considered. It is shown that if certain natural conditions on the rate of decrease of the perturbing potential at arbitrarily high temperatures are violated then the free energy may cease to be analytic. I. We consider a set q~ of translationally invariant (in general, complex-valued) potentials U={UA(z~), A6~(Z~), xA~X~}, (1.1) where ~ is a v-dimensional integral lattice, ~(Z ~) is the set of all finite subsets of Z~, X is some finite set of states of a particle, and X A is the set of configurations xA=(xt; xt6X, t~A). We consider the partition function (with "empty boundary conditions") ZA(U)-~- Z exp{--Hu(xA)}, U6@~, A6~(Zv), (1.2) xAEX A where the Hamiltonian is H~ (xA) 2~ UA (xA), xA E X A (1.3) AcA (here and in what follows, x A is the restriction of the configuration x A to the set A~A). One of the criteria generally adopted in statistical mechanics for the absence of phase transitions for some real-valued potential ~ is the requirement of nonvanishing of the partition function ZA(U

Journal

Theoretical and Mathematical Physics – Springer Journals

Published: May 1, 1988

Keywords: Theoretical, Mathematical and Computational Physics; Applications of Mathematics

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