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Layering and wetting transitions for an SOS interface. (English) Zbl 1209.82011
Summary: We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. There is no bulk external field. The system presents a sequence of layering transitions, whose levels increase with the temperature, before reaching the wetting transition.

82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
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[1] Alexander, K.S., Dunlop, F., Miracle-Sole, S.: Layering in the Ising model. J. Stat. Phys. 141, 217–241 (2010) · Zbl 1202.82015 · doi:10.1007/s10955-010-0042-5
[2] Basuev, A.G.: Ising model in half-space: a series of phase transitions in low magnetic fields. Theor. Math. Phys. 153, 1539–1574 (2007) · Zbl 1139.82309 · doi:10.1007/s11232-007-0132-y
[3] Bissacot, R., Fernandez, R., Procacci, A.: On the convergence of cluster expansions for polymer gases. J. Stat. Phys. 139, 598–617 (2010) · Zbl 1196.82135 · doi:10.1007/s10955-010-9956-1
[4] Binder, K., Landau, D.P.: Wetting versus layering near the roughening transition in the 3d Ising model. Phys. Rev. B 46, 4844 (1992) · doi:10.1103/PhysRevB.46.4844
[5] Cesi, F., Martinelli, F.: On the layering transition of an SOS interface interacting with a wall. I. Equilibrium results. J. Stat. Phys. 82, 823–913 (1996) · Zbl 1042.82512 · doi:10.1007/BF02179794
[6] Chalker, J.T.: The pinning of an interface by a planar defect. J. Phys. A: Math. Gen. 15, L481–L485 (1982) · doi:10.1088/0305-4470/15/9/009
[7] Dobrushin, R.L.: Estimates of semi-invariants for the Ising model at low temperatures. In: Topics in Statistics and Theoretical Physics. Amer. Math. Soc. Transl. (2), vol. 177, pp. 59–81 (1996) · Zbl 0873.60074
[8] Dinaburg, E.I., Mazel, A.E.: Layering transition in SOS model with external magnetic field. J. Stat. Phys. 74, 533–563 (1996) · Zbl 0827.60099 · doi:10.1007/BF02188570
[9] Fröhlich, J., Pfister, C.E.: The wetting and layering transitions in the half-infinite Ising model. Europhys. Lett. 3, 845–852 (1987) · Zbl 1108.82302 · doi:10.1209/0295-5075/3/7/012
[10] Fröhlich, J., Pfister, C.E.: Semi-infinite Ising model: I. Thermodynamic functions and phase diagram in absence of magnetic field. Commun. Math. Phys. 109, 493–523 (1987) · doi:10.1007/BF01206148
[11] Fröhlich, J., Pfister, C.E.: Semi-infinite Ising model: II. The wetting and layering transitions. Commun. Math. Phys. 112, 51–74 (1987) · Zbl 1108.82302 · doi:10.1007/BF01217679
[12] Gallavotti, G., Martin-Lof, A., Miracle-Sole, S.: Some problems connected with the description of coexisting phases at low temperatures in Ising models. In: Lenard, A. (ed.) Mathematical Methods in Statistical Mechanics, pp. 162–202. Springer, Berlin (1973)
[13] Kotecký, R., Preiss, D.: Cluster expansion for abstract polymer systems. Commun. Math. Phys. 103, 491–498 (1986) · Zbl 0593.05006 · doi:10.1007/BF01211762
[14] Lebowitz, J.L., Mazel, A.E.: A remark on the low temperature behavior of an SOS interface in half space. J. Stat. Phys. 84, 379–397 (1996) · Zbl 1081.82545 · doi:10.1007/BF02179648
[15] Miracle-Sole, S.: On the convergence of cluster expansions. Physica A 279, 244–249 (2000) · doi:10.1016/S0378-4371(99)00539-7
[16] Sinai, Ya.G.: Theory of Phase Transitions: Rigorous Results. Pergamon Press, Oxford (1982)
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