Monte Carlo Study of the Widom-Rowlinson Fluid Using Cluster Methods

The Widom-Rowlinson model of a fluid mixture is studied using a new cluster algorithm that is an adaptation of the invaded cluster method previously applied to Potts models. The algorithm overcomes the difficulties of treating continuum hard-core systems and has almost no critical slowing down. Our estimates of byn and gyn for the two-component fluid are consistent with the Ising universality class in two and three dimensions. We also present preliminary results for the three-component fluid. [S0031-9007(97)04175-6] PACS numbers: 05.50. + q, 64.60.Fr, 75.10.Hk Some years ago Widom and Rowlinson [1] introduced a simple continuum model that exhibits a phase transition [2]. The two-component version of this model consists of “black” and “white” particles; particles of the same type do not interact, but particles of differing type experience a hard-core repulsion at separations less than or equal to s [3]. We present a new Monte Carlo method for simulating the Widom-Rowlinson (WR) model and apply the method to study the demixing transition in two and three dimensions. There have been few Monte Carlo studies of the WR critical point because of the difficulties of treating hardcore systems and critical slowing down using standard Monte Carlo techniques. We discuss a new algorithm that overcomes these difficulties using cluster methods of the type introduced by Swendsen and Wang [4]. The algorithm employs the invaded cluster (IC) approach [5,6] to locate the critical point. We find that the algorithm has almost no critical slowing down and that we can obtain accurate values of the critical density and the exponent ratios byn and gyn with modest computational effort. The two-component WR model is expected to be in the Ising universality class. Our results for byn and gyn are consistent with this assumption, and our value for the critical density of the three-dimensional ( d › 3 )W R model agrees with recent results obtained in Ref. [7]. We also consider a WR model in which there are q components, any two of which interact via a hard-core repulsion [8,9]. Our algorithm easily extends to these q-component WR models, and we present results for the three-component model in d › 2, 3. Graphical representations of the WR model. — A configuration of the WR fluid consists of two sets of points, S and T , corresponding to the positions of the black and white particles. In the grand canonical ensemble, the probability density for finding the configuration sS, Td is