This volume is an extended version of the lecture notes prepared for the course Capita selecta theoretische fysica during the first semester of the academic year 1995/96 at the Katholieke Universiteit Leuven. The selection of the material and the form of its presentation are, naturally, predetermined by the taste and experience of the author. The attempted goal was three-fold. First, to present a formulation of the hypotheses of finite-size scaling in a unified way, which does not discriminate between short- and long-range interactions, nor between the standard scaling and its modification above the upper critical dimension.
Second, to demonstrate that these hypotheses stand an extensive test on simplest exactly solved models. The mean spherical model with power-law interaction seems suitable for that purpose since it interpolates between the extremities: nearest-neighbours and equivalent-neighbours interactions. Due to its simplicity, a large class of equivalent-neighbours models is considered too. It offers the possibility of deriving finite-size scaling from the Burgers equation for the magnetization, and yields a convenient illustration of the probabilistic view on finite-size scaling.
The third aim was to acquaint the reader with some analytical techniques which, hopefully, might be useful in the consideration of more general finite-size problems.
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