Abstract
When several phases coexist, the interface between two phases can be wetted by several films of the other phases. This is calledmultilayer wetting and can be characterized by the behavior of thespreading coefficients, which relate the surface tensions between the different phases. In this paper we consider a class of models which can exhibit a sequence of phase transitions. With some new correlation inequalities, we prove the positivity of a family of spreading coefficients. These inequalities, together with a thermodynamic argument, lead to the conclusion of multilayer wetting. These results generalize earlier results where single-layer interfacial wetting was obtained for the Potts model.
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References
J. De Coninck, A. Messager, S. Miracle-Solé, and J. Ruiz, A study of perfect wetting for Potts and Blume-Capel models with correlation inequalities,J. Stat. Phys. 52:45 (1988).
R. J. Baxter, Potts model at the critical temperature,J. Phys. C: Solid State Phys. 6:L445 (1973).
R. Kotecký and S. B. Shlosman, First order phase transitions in large entropy lattice models,Commun. Math. Phys. 83:493 (1982).
J. Bricmont, J. L. Lebowitz, and K. Kuroda, First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory,Commun. Math. Phys. 101:501 (1985).
L. Laanait, A. Messager, and J. Ruiz, Phase coexistence and surface tensions for the Potts model,Commun. Math. Phys. 105:527 (1986).
R. Kotecký, L. Laanait, A. Messager, and J. Ruiz, Theq-state Potts model in the standard Pirogov-Sinai theory,J. Stat. Phys. 58:199 (1990).
R. H. Schonmann, On two correlation inequalities for Potts models,J. Stat. Phys. 52:61 (1988).
A. Messager, S. Miracle-Solé, J. Ruiz, and S. Shlosman, Interfaces in the Potts model, preprint MarSeille CPT/89.
J. Ginibre, General formulation of Griffiths inequalities,Commun. Math. Phys. 16:310 (1970).
F. Dunlop, Correlation inequalities for multicomponent rotators,Commun. Math. Phys. 49:247 (1976).
H. Kunz, C. E. Pfister, and P. A. Vuillermot, Correlation inequalities for some classical vector models,Phys. Lett. 54A:428 (1975),J. Phys. A: Math. Gen. 9:1673 (1976).
G. Gallavotti, A. Martin Löf, and S. Miracle-Solé, Some problems connected with the coexistence of phases in the Ising model, inStatistical Mechanics and Mathematical Problems (Springer, Berlin, 1973).
J. Bricmont and J. L. Lebowitz, Wetting in Potts and Blume-Capel models,J. Stat. Phys. 46:1015 (1987).
C. E. Pfister, Translation invariant equilibrium states in ferromagnetic Abelian systems,Commun. Math. Phys. 86:375 (1982).
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On leave from Centre de Physique Théorique (CNRS-UPR14), Ecole Polytechnique, 91128 Palaiseau, France.
On leave from Ecole Normale Supérieure, Takaddoum Rabat, Morocco.
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Dunlop, F., Laanait, L., Messager, A. et al. Multilayer wetting in partially symmetricq-state models. J Stat Phys 59, 1383–1396 (1990). https://doi.org/10.1007/BF01334756
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DOI: https://doi.org/10.1007/BF01334756