Physics – Mathematical Physics
Scientific paper
2005-05-03
Commun. Math. Phys. 264 (2006), no. 3, 631-656
Physics
Mathematical Physics
26 pages
Scientific paper
10.1007/s00220-006-1523-x
Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the "transitional gap" are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria.
Biskup Marek
Kotecky Roman
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