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

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

2007-06-28

arxiv.org/abs/0706.4148v2

Rev. Math. Phys. 20, 335-365, (2008)

Physics

Mathematical Physics

29 pages, Section 5 added, to appear in Rev. Math. Phys

Scientific paper

10.1142/S0129055X08003298

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).

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