Critical manifold of globally coupled overdamped anharmonic oscillators driven by additive Gaussian white noise

摘要

We consider an infinite array of globally coupled overdamped anharmonic oscillators subject to additivenGaussian white noise which is closely related to the mean field u00024-Ginzburg-Landau model. We prove thenexistence of a well-behaved critical manifold in the parameter space which separates a symmetric phase fromna symmetry broken phase. Given two of the system parameters, there is a unique critical value of the third.nThe proof exploits that the critical control parameter ac is bounded by its limit values for weak and strongnnoise. In these limits, the mechanism of symmetry breaking differs. For weak noise, the distribution is Gaussiannand the symmetry is broken as the whole distribution is shifted in either the positive or the negative direction.nFor strong noise, there is a symmetric double-peak distribution and the symmetry is broken as the weights ofnthe peaks become different. We derive an ordinary differential equation whose solution describes the criticalnmanifold. Using a series ansatz to solve this differential equation, we determine the critical manifold for weaknand strong noise and compare it to numerical results.We derive analytic expressions for the order parameter andnthe susceptibility close to the critical manifold.