Mechanism of symmetry breaking in the spherical limit: Phase coherence in finite-size systems

Abstract

The appearance of symmetry breaking in the thermodynamic limit is studied from a dynamical point of view. We solved the time-dependent Landau-Ginzburg model in the spherical limit and show that the finite-size system develops a phase-coherence phenomenon analogous to that appearing in lasers. Below the critical point of the infinite system the orientational diffusion of the magnetization becomes the slowest mode and its time scale is well separated from all the other relaxational mechanisms. As expected, this phase diffusion freezes in completely in the thermodynamic limit.