Abstract
I use Israel's methods to prove new theorems of "ubiquitous pathology" for classical and quantum lattice systems. The main result is the following: Let Φ be any interaction and ρ{variant} be any translation-invariant equilibrium state for Φ (extremal or not). Then there exists a sequence {Φk} of interactions converging to Φ, having extremal (or even unique) translation-invariant equilibrium states ρ{variant}k, such that {ρ{variant}k} converges to ρ{variant}. In certain situations the perturbations Φk-Φ can be chosen to lie in a cone of "antiferromagnetic pair interactions." I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r2 interaction (Thouless effect).
Original language | English (US) |
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Pages (from-to) | 327-336 |
Number of pages | 10 |
Journal | Communications In Mathematical Physics |
Volume | 86 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1982 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics