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Widom-Rowlinson model (continuum and lattice)  [PDF]
L. Samaj
Physics , 2007,
Abstract: This is a short review about liquid-vapor and crystalline phase transitions in continuum and lattice Widom-Rowlinson models.
Critical Behavior of the Widom-Rowlinson Lattice Model  [PDF]
Ronald Dickman,George Stell
Physics , 1995, DOI: 10.1063/1.468970
Abstract: We report extensive Monte Carlo simulations of the Widom-Rowlinson lattice model in two and three dimensions. Our results yield precise values for the critical activities and densities, and clearly place the critical behavior in the Ising universality class.
Direct correlation functions of the Widom-Rowlinson model  [PDF]
R. Fantoni,G. Pastore
Physics , 2003, DOI: 10.1016/j.physa.2003.10.012
Abstract: We calculate, through Monte Carlo numerical simulations, the partial total and direct correlation functions of the three dimensional symmetric Widom-Rowlinson mixture. We find that the differences between the partial direct correlation functions from simulation and from the Percus-Yevick approximation (calculated analytically by Ahn and Lebowitz) are well fitted by Gaussians. We provide an analytical expression for the fit parameters as function of the density. We also present Monte Carlo simulation data for the direct correlation functions of a couple of non additive hard sphere systems to discuss the modification induced by finite like diameters.
Structure and phase equilibria of the Widom-Rowlinson model  [PDF]
J. M. Brader,R. L. C. Vink
Physics , 2008, DOI: 10.1088/0953-8984/19/3/036101
Abstract: The Widom-Rowlinson model plays an important role in the statistical mechanics of second order phase transitions and yet there currently exists no theoretical approach capable of accurately predicting both the microscopic structure and phase equilibria. We address this issue using computer simulation, density functional theory and integral equation theory. A detailed study of the pair correlation functions obtained from computer simulation motivates a closure of the Ornstein-Zernike equations which gives a good description of the pair structure and locates the critical point to an accuracy of 2 percent.
Dynamical Widom-Rowlinson model and its mesoscopic limit  [PDF]
Dmitri Finkelshtein,Yuri Kondratiev,Oleksandr Kutoviy,Maria Joao Oliveira
Physics , 2014, DOI: 10.1007/s10955-014-1124-6
Abstract: We consider the non-equilibrium dynamics for the Widom-Rowlinson model (without hard-core) in the continuum. The Lebowitz-Penrose-type scaling of the dynamics is studied and the system of the corresponding kinetic equations is derived. In the space-homogeneous case, the equilibrium points of this system are described. Their structure corresponds to the dynamical phase transition in the model. The bifurcation of the system is shown.
Monte Carlo study of the Widom-Rowlinson fluid using cluster methods  [PDF]
Gregory Johnson,Harvey Gould,J. Machta,L. K. Chayes
Physics , 1997, DOI: 10.1103/PhysRevLett.79.2612
Abstract: The Widom-Rowlinson model of a fluid mixture is studied using a new cluster algorithm that is a generalization of the invaded cluster algorithm previously applied to Potts models. Our estimate of the critical exponents for the two-component fluid are consistent with the Ising universality class in two and three dimensions. We also present results for the three-component fluid.
Ising meets Ornstein and Zernike, Debye and Hückel, Widom and Rowlinson, and others
Dickman, Ronald;
Brazilian Journal of Physics , 2000, DOI: 10.1590/S0103-97332000000400014
Abstract: the name ising has come to stand not only for a specific model, but for an entire universality class - arguably the most important such class - in the theory of critical phenomena. i review several examples, both in and out of equilibrium, in which ising universality appears or is pertinent. the "ornstein-zernike" connection concerns a thermodynamically self-consistent closure of the eponymous relation, which lies at the basis of the modern theory of liquids, as applied to the ising lattice gas. debye and hückel founded the statistical mechanics of ionic solutions, which, despite the long-range nature of the interaction, now appear to exhibit ising-like criticality. the model of widom and rowlinson involves only excluded-volume interactions between unlike species, but again belongs to the ising universality class. far-from-equilibrium models of voting behavior, catalysis, and hysteresis provide further examples of this ubiquitous universality class.
Ising meets Ornstein and Zernike, Debye and Hückel, Widom and Rowlinson, and others  [cached]
Dickman Ronald
Brazilian Journal of Physics , 2000,
Abstract: The name Ising has come to stand not only for a specific model, but for an entire universality class - arguably the most important such class - in the theory of critical phenomena. I review several examples, both in and out of equilibrium, in which Ising universality appears or is pertinent. The "Ornstein-Zernike" connection concerns a thermodynamically self-consistent closure of the eponymous relation, which lies at the basis of the modern theory of liquids, as applied to the Ising lattice gas. Debye and Hückel founded the statistical mechanics of ionic solutions, which, despite the long-range nature of the interaction, now appear to exhibit Ising-like criticality. The model of Widom and Rowlinson involves only excluded-volume interactions between unlike species, but again belongs to the Ising universality class. Far-from-equilibrium models of voting behavior, catalysis, and hysteresis provide further examples of this ubiquitous universality class.
Ising Meets Ornstein and Zernike, Debye and Huckel, Widom and Rowlinson, and Others  [PDF]
Ronald Dickman
Physics , 2000,
Abstract: The name Ising has come to stand not only for a specific model, but for an entire universality class - arguably the most important such class - in the theory of critical phenomena. I review several examples, both in and out of equilibrium, in which Ising universality appears or is pertinent. The "Ornstein-Zernike" connection concerns a thermodynamically self-consistent closure of the eponymous relation, which lies at the basis of the modern theory of liquids, as applied to the Ising lattice gas. Debye and Huckel founded the statistical mechanics of ionic solutions, which, despite the long-range nature of the interaction, now appear to exhibit Ising-like criticality. The model of Widom and Rowlinson involves only excluded-volume interactions between unlike species, but again belongs to the Ising universality class. Far-from-equilibrium models of voting behavior, catalysis, and hysteresis provide further examples of this ubiquitous universality class.
Critical behavior of the Widom-Rowlinson mixture: coexistence diameter and order parameter  [PDF]
R. L. C. Vink
Physics , 2006, DOI: 10.1063/1.2171191
Abstract: The critical behavior of the Widom-Rowlinson mixture [J. Chem. Phys. 52, 1670 (1970)] is studied in d=3 dimensions by means of grand canonical Monte Carlo simulations. The finite size scaling approach of Kim, Fisher, and Luijten [Phys. Rev. Lett. 91, 065701 (2003)] is used to extract the order parameter and the coexistence diameter. It is demonstrated that the critical behavior of the diameter is dominated by a singular term proportional to t^(1-alpha), with t the relative distance from the critical point, and alpha the critical exponent of the specific heat. No sign of a term proportional to t^(2beta) could be detected, with beta the critical exponent of the order parameter, indicating that pressure-mixing in this model is small. The critical density is measured to be rho*sigma^3 = 0.7486 +/- 0.0002, with sigma the particle diameter. The critical exponents alpha and beta, as well as the correlation length exponent nu, are also measured and shown to comply with d=3 Ising criticality.
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