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Communications in Mathematical Physics

, Volume 42, Issue 1, pp 9–28 | Cite as

On the Landau diamagnetism

  • N. Angelescu
  • G. Nenciu
  • M. Bundaru
Article

Abstract

The grand-canonical partition function of an assembly of free spinless electrons in a magnetic field enclosed in a box (Dirichlet boundary conditions) is shown to be an entire function of the fugacityz and the magnetic fieldH, as a consequence of the trace-norm convergence of the perturbation series for the statistical semigroup. This allows to derive analyticity properties of the pressure as a function ofz andH, and to express the coefficients of its power series expansion aroundz=H=0 by means of the unperturbed semigroup. Hence, the magnetic susceptibility at zero field and fixed density is expressed in terms of Green functions of the heat equation. Its asymptotic expansion for Λ→∞ (Fisher) along parallelepipedic domains is obtained up to 0 (S(Λ)/V(Λ)). The volume term of this expansion is the Landau diamagnetism.

Keywords

Partition Function Magnetic Susceptibility Power Series Asymptotic Expansion Green Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • N. Angelescu
    • 1
  • G. Nenciu
    • 1
  • M. Bundaru
    • 2
  1. 1.Institute for Atomic PhysicsBucharestRomania
  2. 2.Institute of PhysicsBucharestRomania

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