Abstract
We review the statistical mechanics of two-dimensional interfaces separating phases in ℤ3, with particular attention to constructive aspects, understood here as the construction of convergent expansions for the free energy and correlation functions. These will take different forms depending on whether the interface is rigid, like in the three-dimesional Ising model at low temperature, or rough like in the capillary waves model. The corresponding techniques may be associated respectively to the Pirogov-Sinai theory or to perturbations of a massless gaussian field. The unifying feature is the occurrence of scaled expansions, which may allow to control the neighborhood of a phase transition. Some open problems are presented and discussed.
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Dunlop, F. (1995). Random and interacting surfaces. In: Rivasseau, V. (eds) Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics. Lecture Notes in Physics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59190-7_32
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DOI: https://doi.org/10.1007/3-540-59190-7_32
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