Lattice systems with a continuous symmetry - III. Low temperature asymptotic expansion for the plane rotator model

Jean Bricmont; Jean Raymond Fontaine; Joel L. Lebowitz; Elliott H. Lieb; Thomas Spencer

doi:10.1007/BF02046764

Lattice systems with a continuous symmetry - III. Low temperature asymptotic expansion for the plane rotator model

Jean Bricmont, Jean Raymond Fontaine, Joel L. Lebowitz, Elliott H. Lieb, Thomas Spencer

Mathematics

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37 Scopus citations

Abstract

We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d=3.

Original language	English (US)
Pages (from-to)	545-566
Number of pages	22
Journal	Communications In Mathematical Physics
Volume	78
Issue number	4
DOIs	https://doi.org/10.1007/BF02046764
State	Published - Jan 1981

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02046764

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abstract = "We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d=3.",

author = "Jean Bricmont and Fontaine, {Jean Raymond} and Lebowitz, {Joel L.} and Lieb, {Elliott H.} and Thomas Spencer",

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AU - Lieb, Elliott H.

AU - Spencer, Thomas

PY - 1981/1

Y1 - 1981/1

N2 - We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d=3.

AB - We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d=3.

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Lattice systems with a continuous symmetry - III. Low temperature asymptotic expansion for the plane rotator model

Abstract

All Science Journal Classification (ASJC) codes

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