Particle Systems and Reaction-Diffusion Equations

Abstract

In this paper we will consider translation invariant finite range particle systems with state space $\{0, 1,\ldots,\kappa - 1\}^S$ with $S = \varepsilon \mathbb{Z}^d$. De Masi, Ferrari and Lebowitz have shown that if we introduce stirring at rate $\varepsilon^{-2}$, then the system converges to the solution of an associated reaction diffusion equation. We exploit this connection to prove results about the existence of phase transitions when the stirring rate is large that apply to a wide variety of examples with state space $\{0, 1\}^S$.