Phase Transitions, Scale Invariance, Renormalization Group Theory, and Percolation

Abstract

This chapter builds upon the results of the two preceding chapters dealing with the ferromagnetic phase transition and the gas-liquid transition. We start with some general considerations on symmetry breaking and phase transitions. Then a variety of phase transitions and critical points are discussed, and analogous behavior is pointed out. Subsequently, we deal in detail with critical behavior and give its phenomenological description in terms of static scaling theory. In the section that follows, we discuss the essential ideas of renormalization group theory on the basis of a simple model, and use it to derive the scaling laws. Finally, we introduce the Ginzburg-Landau theory; it provides an important cornerstone for the various approximation methods in the theory of critical phenomena.KeywordsPartition FunctionRenormalization GroupIsing ModelCritical ExponentPercolation ThresholdThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.