Geometrical approach to phase transitions in frustrated and unfrustrated systems

Abstract

We review the basic ideas which have been developed to characterize geometrically the equilibrium phase transitions. This approach elucidates many concepts like propagation of correlations, upper critical dimensionality, breakdown of hyperscaling, strong universality, and other basic ideas in phase transitions. More recently the extension of the geometrical approach to frustrated systems like spin glasses has lead to the definition of a new geometrical model called frustrated percolation. Application of this model to complex systems such as glasses and granular materials is also briefly reviewed.