Statistical Mechanics of Interfaces

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The main purpose of the traditional statistical physics has been, in general, to explain macroscopic phenomena in terms of features of microscopic elements of the material, like atoms and molecules. However, in these processes, one often faces a difficulty particularly in the problems where long-range interactions play an essential role, e. g. phase transition phenomena. In such problems, it is often useful to adopt coarse-grained descriptions. A typical example is the critical phenomena.In this study, we start from a macroscopic continuum model, called Ginzburg-Landau model, which can be derived. by coarse-graining microscopic models. Such a continuum description is sometimes inadequate and should be supplemented by taking account of localized singularities, like interfaces. We studied the following problems, in each of which interafces play a crucial role ;1) Statistical Mechanics of Cellular Pattern Formation2) Phase Coexistence of Gels3) Pattern Formation in Sytems Containing SurfactantsThese problems are important not only in the field of fundamental physics but also in the field of applied sciences. Some of our researches has exploratory aspects, which should be refined in the future studies.