 96136 Brydges, D.C., Slade, G.
 Statistical mechanics of the 2dimensional
focussing nonlinear Schroedinger equation
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Apr 17, 96

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Abstract. We study a natural construction of an invariant
measure for the 2dimensional periodic focussing nonlinear
Schr\"odinger equation, with the critical cubic nonlinearity. We find
that a phase transition occurs as the coupling constant defining the
strength of the nonlinearity is increased, but that the natural
construction, successful for the 1dimensional case and for the
2dimensional defocussing case, cannot produce an invariant measure.
Our methods rely on an analysis of a statistical mechanical model
closely related to the spherical model of Berlin and Kac.
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