A new method for the thermodynamics of the BCS model
type: Item
instance of: scholarly article
title: A new method for the thermodynamics of the BCS model
zbMATH Open document ID: 0658.60141
DOI: 10.1007/BF01466728
author: N. G. Duffield
author: Joe V. Pulé
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: The authors analyze a simplified version of the B.C.S. - model to understand phase transitions. Although Bogolyubov and his school have developed perturbative methods to analyze the full B.C.S.-model, these are rigorously valid only in the limiting case of zero temperature. The authors deal with a quasi-spin model, with variable energy and coupling terms. The method used is based on the recent applications of Varadhan's large deviation principle to quasi-spin systems by \textit{W. Cegla}, \textit{J. T. Lewis} and \textit{G. A. Raggio} [Commun. Math. Phys. 118, No.2, 337-354 (1988)] and the Berzin-Lieb estimates for the free energy. The technique consists in introducing a large number of subsystems and approximating the subsystem hamiltonian by a total spin hamiltonian. This approximation is shown to converge when the number of subsystems goes to infinity. This limit and the thermodynamic limit are shown to commute. The variational principle arising from the application of the large deviation principle is shown to yield the gap equation. The existence of bifurcation at a critical parameter value is demonstrated. It is shown that the order parameter does not vanish below this critical temperature.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 4076283
zbMATH Keywords: phase transitions
zbMATH Keywords: quasi-spin model
zbMATH Keywords: large deviation principle
zbMATH Keywords: quasi- spin systems
zbMATH Keywords: thermodynamic limit
zbMATH Keywords: existence of bifurcation at a critical parameter value
MaRDI profile type: Publication
cites work: Thermodynamics of the BCS model through large deviations
cites work: The equilibrium thermodynamics of a spin-boson model.
cites work: Asymptotic probabilities and differential equations
cites work: Q3681702
cites work: The classical limit of quantum partition functions
cites work: The classical limit of quantum spin systems
cites work: Theory of Superconductivity
cites work: Q3287168
cites work: The mathematical structure of the bardeen-cooper-schrieffer model
cites work: On the asymptotic exactness of the Bogoliubov approximation for many boson systems
full work available at URL: https://doi.org/10.1007/bf01466728
OpenAlex ID: W2052324123
Recommended article: Thermodynamics of the BCS model through large deviations
Recommended article: BCS model in Tsallis' statistical framework
Recommended article: THE ELEMENTARY EXCITATIONS OF THE BCS MODEL IN THE CANONICAL ENSEMBLE
Recommended article: A new approach to phase transitions, thermodynamics, and hydrodynamics
Recommended article: On (b,c)-system at finite temperature in thermo field approach
Recommended article: The critical temperature for the BCS equation at weak coupling
Recommended article: The large-deviation principle and the BCS model
Recommended article: Q5321097
Recommended article: Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics
description: scientific article; zbMATH DE number 4076283