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.