The Role of Noise in Systems with Two Symmetric Absorbing States

For such systems a phenomenological Langevin equation has been proposed which has been shown to encompass all the observed critical behaviour. In essence this is achieved by varying the shape of the potential from which the drift term is derived in the Langevin equation. In this talk I will outline a microscopic model which explicitly allows us to vary the noise strength without altering the shape of the potential. By transformation of the spatially discrete Langevin equation obtained for this model from one with multiplicative noise to one with additive noise, a simpler diffusive potential picture is obtained. From this we observe the possibility of different ordering behaviour of the system according to the value of h which sets the strength of the noise in our model, and make lower bound predictions for h*, the transition point between the two ordering regimes. Finally, time permitting, I will derive the Allen-Cahn equation for curvature-driven coarsening which has formed the basis of our simulations.