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I consider several Langevin and Fokker-Planck classes of dynamics for scalarfield theories in contact with a thermal bath at temperature T. These modelshave been applied recently in the numerical description of the dynamics ofsecond order phase transitions and associated topological defect formation aswell as in other studies of these critical phenomena. Closed form solutions ofthe Fokker-Planck equation are given for the harmonic potential and a dynamicalmean-field approximation is developed. These methods allow for an analyticaldiscussion of the behavior of the theories in several circumstances of interestsuch as critical slowing down at a second order transition and the developmentof spinodal instabilities. These insights allow for a more detailedunderstanding of several numerical studies in the literature.Comment: 10 pages, no figures, uses RevTe

Properties of the Langevin and Fokker-Planck equations for scalar fields and their application to the dynamics of second order phase transitions