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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REFERENCES
M. Aizenman, On the slow decay of O(2) correlations in the absence of topological excitations: remark on the Patrascioiu-Seiler model, J. Stat. Phys. 77:351-359 (1994).
J. van den Berg and C. Maes, Disagreement percolation in the study of Markov fields, Ann. Probab. 22:749-763 (1994).
G. R. Brightwell, O. Häggström, and P. Winkler, Nonmonotonic behavior in hardcore and Widom-Rowlinson models, J. Stat. Phys. 94:415-435 (1998).
L. Chayes, R. Kotecký, and S. Shlosman, Aggregation and intermediate phases in dilute spin systems, Commun. Math. Phys. 171:203-232 (1995).
L. Chayes, R. Koteckyý, and S. Shlosman, Staggered phases in diluted systems with continuous spins, Commun. Math. Phys. 189:631-640 (1997).
R. L. Dobrushin and S. B. Shlosman, Phases corresponding to minima of the local energy, Selecta Math. Sov. 1:317-338 (1981).
J. Fröhlich and D. A. Huckaby, Percolation in hard-core lattice gases and a model ferrofluid, J. Stat. Phys. 38:809-821 (1985).
M. Fukuyama, Discrete symmetry breaking for certain short-range interactions, J. Stat. Phys. 98:1049-1061 (2000).
H.-O. Georgii, Gibbs Measures and Phase Transitions (de Gruyter, Berlin/New York, 1998).
H.-O. Georgii, O. Häggström, and C. Maes, The random geometry of equilibrium phases, in Phase Transitions and Critical Phenomena, Vol. 18, Domb and J. L. Lebowitz, eds. (Academic Press, 2000).
R. Kotecký and S. Shlosman, First-order phase transitions in large entropy lattice systems, Commun. Math. Phys. 83:493-550 (1982).
J. L. Lebowitz and G. Gallavotti, Phase transition in binary lattice gases, J. Math. Phys. 12:1129-1133 (1971).
J. L. Lebowitz, A. Mazel, P. Nielaba, and L. Šamaj, Ordering and demixing transitions in multicomponent Widom-Rowlinson models, Phys. Rev. E 52:5985-5996 (1995).
P. Nielaba and J. L. Lebowitz, Phase transitions in the multicomponent Widom-Rowlinson model and in hard cubes on the BCC-lattice, Physica A 244:278-284 (1997).
A. Patrascioiu and E. Seiler, Phase structure of two-dimensional spin models and percolation, J. Stat. Phys. 69:573-595 (1992).
D. Ruelle, Thermodynamic Formalism (Addison-Wesley, Reading).
L. K. Runnels and J. L. Lebowitz, Phase transitions of a multicomponent Widom-Rowlinson model, J. Math. Phys. 15:1712-1717 (1974).
S. B. Shlosman, The method of reflection positivity in the mathematical theory of first-order phase transitions, Russ. Math. Surveys 41(3):83-134 (1986).
B. Widom and J. S. Rowlinson, New model for the study of liquid-vapor phase transition, J. Chem. Phys. 52:1670-1684 (1970).
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Georgii, HO., Zagrebnov, V. Entropy-Driven Phase Transitions in Multitype Lattice Gas Models. Journal of Statistical Physics 102, 35–67 (2001). https://doi.org/10.1023/A:1026556508220
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DOI: https://doi.org/10.1023/A:1026556508220