Disoriented chiral condensate in the presence of dissipation and noise

We have investigated the phase transition and disoriented chiral condensate domain formation in linear $\ensuremath{\sigma}$ model. Solving the Langevin equation for the linear $\ensuremath{\sigma}$ model, we have shown that, for zero mass pions, the $\ensuremath{\sigma}$-model fields undergo a phase transition above a certain temperature ${(T}_{c}).$ For finite mass pions, there is no phase transition. It was also shown that for zero mass pions, $\ensuremath{\sigma}$-model fields, thermalized at a temperature above ${T}_{c},$ when cooled down rapidly, disoriented chiral condensate domains are formed, quite late in the evolution. For massive pions, no large disoriented chiral condensate domain is formed.