Statistical mechanics of a discrete nonlinear system

Statistical mechanics of the discrete nonlinear Schrodinger equation is stu died by means of analytical and numerical techniques. The lower bound of th e Hamiltonian permits the construction of standard Gibbsian equilibrium mea sures for positive temperatures. Beyond the line of T = infinity, we identi fy a phase transition through a discontinuity in the partition function. Th e phase transition is demonstrated to manifest itself in the creation of br eatherlike localized excitations. Interrelation between the statistical mec hanics and the nonlinear dynamics of the system is explored numerically in both regimes.