We argue that certain aspects of conventional thermodynamics are valid only for temperatures larger than the mean energy level spacing for a finite quantum fermion system (the Kubo particle) and evaluate its heat capacity and spin susceptibility.

Physica ScriptaJan 1, 19966 citations

arXiv:physics/0507055 · European Journal of Physics

Introduction to thermodynamics of spin models in the Hamiltonian limit

Bertrand Berche, Alexander López

Published Nov 9, 2005• 1 citation

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Abstract

DOI: 10.1088/0143-0807/27/1/003

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Introduction to thermodynamics of spin models in the Hamiltonian limit

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A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit.Emphasis is on the construction of the relevant Hamiltonian, and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices.The targeted students are those of a graduate statistical physics course Résumé.On donne une description didactique des propriétés thermodynamiques de systèmes de spins classiques en termes de leur équivalent quantique dans la limite hamiltonienne.On insiste sur la construction de l'hamiltonien et le calcul des moyennes thermiques est effectué explicitement dans le cas de systèmes de petite taille, décrits dans la théorie hamiltonienne des champs par des petites matrices.Le public visé est celui d'étudiants suivant un cours avancés en physique statistique.A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit.Emphasis is on the construction of the relevant Hamiltonian, and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices.The targeted students are those of a graduate statistical physics course Résumé.On donne une description didactique des propriétés thermodynamiques de systèmes de spins classiques en termes de leur équivalent quantique dans la limite hamiltonienne.On insiste sur la construction de l'hamiltonien et le calcul des moyennes thermiques est effectué explicitement dans le cas de systèmes de petite taille, décrits dans la théorie hamiltonienne des champs par des petites matrices.Le public visé est celui d'étudiants suivant un cours avancés en physique statistique.

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s\rightarrow \infty

s → ∞ . As expected, a good agreement is obtained, except for the low temperature region. However, this region shrinks with increasing s, so that the classical state variables emerge as envelopes of the quantum mechanical ones.