Entropy-Driven Phase Transitions in Multitype Lattice Gas Models |
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Authors: | Hans-Otto Georgii Valentin Zagrebnov |
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Affiliation: | (1) Mathematisches Institut der Universität München, Theresienstr. 39, D-80333 München, Germany;(2) Université de la Méditerranée and Centre de Physique Théorique, CNRS-Luminy-Case 907, 13288 Marseille Cedex 9, France |
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Abstract: | In multitype lattice gas models with hard-core interaction of Widom–Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and the activity of particles. We investigate this phenomenon in four different models on the square lattice: the multitype Widom–Rowlinson model with diamond-shaped resp. square-shaped exclusion between unlike particles, a Widom–Rowlinson model with additional molecular exclusion, and a continuous-spin Widom–Rowlinson model. In each case we show that this competition leads to a first-order phase transition at some critical value of the activity, but the number and character of phases depend on the geometry of the model. We also analyze the typical geometry of phases, combining percolation techniques with reflection positivity and chessboard estimates. |
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Keywords: | first-order phase transition entropy-energy conflict staggered phase Widom– Rowlinson lattice gas plane-rotor model ferrofluid percolation chessboard estimate reflection positivity |
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