Free energy density for mean field perturbation of states of a one-dimensional spin chain

Fumio Hiai, Milán Mosonyi, Hiromichi Ohno, Dénes Petz

Research output: Contribution to journalArticle

7 Citations (Scopus)


Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).

Original languageEnglish
Pages (from-to)335-365
Number of pages31
JournalReviews in Mathematical Physics
Issue number3
Publication statusPublished - Apr 1 2008



  • Finitely correlated states
  • Free energy density
  • Gibbs states
  • Interactions
  • KMS states
  • Legendre transform
  • Mean relative entropy
  • Quantum Markov states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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