Local thermodynamical stability of Fermion lattice systems

Huzihiro Araki, Hajime Moriya

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Within the framework for equilibrium statistical mechanics of Fermion lattice systems formulated in our preceding work, we study the local thermodynamical stability (LTS) as an alternative characterization of equilibrium states, which works without the translation invariance assumption for the states. We propose two versions, called LTS-M (mathematical) and LTS-P (physical) according to the choice of the algebra of the outside system for a local region I, LTS-M for the commutant of the local subalgebra A(I) and LTS-P for the subalgebra A(Ic) for the complementary region Ic of I. We show that the two conditions are equivalent for even states, evenness referring to Fermion numbers. By applying known methods of proof by Sewell and Araki, the following results are obtained: (1) The LTS-M condition implies the dKMS condition for a general state φ for an arbitrary general potential (in our technical sense). The same statement holds for the LTS-P condition if φ is even. (2) The LTS-M or LTS-P condition for a translation invariant state implies that the state is a solution of the variational principle for any translation covariant standard potential.

Original languageEnglish
Pages (from-to)33-45
Number of pages13
JournalLetters in Mathematical Physics
Volume62
Issue number1
DOIs
Publication statusPublished - 2002 Oct
Externally publishedYes

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fermions
variational principles
statistical mechanics
invariance
algebra

Keywords

  • Equilibrium statistical mechanics
  • Fermion lattice systems
  • Local stability

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Local thermodynamical stability of Fermion lattice systems. / Araki, Huzihiro; Moriya, Hajime.

In: Letters in Mathematical Physics, Vol. 62, No. 1, 10.2002, p. 33-45.

Research output: Contribution to journalArticle

Araki, Huzihiro ; Moriya, Hajime. / Local thermodynamical stability of Fermion lattice systems. In: Letters in Mathematical Physics. 2002 ; Vol. 62, No. 1. pp. 33-45.
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