Statistical Physics and Condensed Matter

Phase Transitions inDisordered Systems

Reimer Kühn, Giorgio Mazzeo


Disordered systems are characterized by two types of variables, configurational degrees of freedom describing the fixed composition of the system under investigation, which usually depends on a preparation process, and dynamical variables proper, by which one denotes those degrees freedom which evolve rapidly on time-scales set by experimental conditions and so attain a thermodynamic equilibrium which depends parametrically on the fixed configuration. Within this project we investigate whether disorder has an influence on the signatures of phase transitions, and if so, to what extent. Currently we are investigating the simplest form of disorder - random spin dilution - and its influence on the transition to ferromagnetic order. One of the questions being investigated is whether disorder will modify the critical exponents of the transition relative to those of the corresponding pure system. A general answer to this question is known for infinitesimally weak disorder. If, on the other hand, disorder is no longer infinitesimally weak, little is known, and the question whether disorder will modify e.g. crititical exponents of the two-dimensional Ising model has remained unsettled for more than 25 years. We are investigating this system using numerical trasfer-matrix and renormalization group methods, in combination with a generalized grand ensemble approach by which disordered systems can be mapped onto ordered ones in a suitably enlarged phase space.

Recent Papers 17.10.1999