Below is the ascii version of the abstract for 04-121.
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A.C.D.van Enter, S.B.Shlosman
Provable first-order transitions for nonlinear vector and
gauge models with continuous symmetries.
(46K, latex, )
ABSTRACT. we consider various sufficiently nonlinear vector models of
ferromagnets, of nematic liquid crystals and of nonlinear lattice gauge theories with continuous symmetries. We show, employing the method of
Reflection Positivity and Chessboard Estimates, that they all exhibit
first-order transitions in the temperature, when the nonlinearity
parameter is large enough.The results hold in dimnsion 2 or more for
the ferromagnetic models and the RP^{N-1} liquid crystal models
and in dimension 3 or moe for the lattice gauge models. In the
two-dimensional case our results clarify and solve a recent controversy
about the possibility of such transitions. for lattice gauge models
our methods provide the first proof of a first-order transition
in a model with a continuous gauge symmtery.