A Phase Transition in a Widom-Rowlinson Model with Curie-Weiss Interaction

摘要

An analog of the continuum Widom-Rowlinson model is introduced and studied.Its two-component version is a gas of point particles of types 0 and 1 placedin $\mathds{R}^d$, in which like particles do not interact and unlike particlescontained in a vessel of volume $V$ repel each other with intensity $a/V$. Theone-component version is a gas of particles with multi-particle interactions ofCurie-Weiss type. Its thermodynamic behavior is obtained by integrating out thecoordinates of one of the components of the two-component version. In the grandcanonical setting, a rigorous theory of phase transitions in this model isdeveloped and discussed. In particular, for both versions thermodynamic phasesand phase diagrams are explicitly constructed and the equations of state areobtained and analyzed.