Nishimori point in random-bond Ising and Potts models in 2D

We study the universality class of the fixed points of the 2D random bond q-state Potts model by means of numerical transfer matrix methods. In particular, we determine the critical exponents associated with the fixed point on the Nishimori line. Precise measurements show that the universality class of this fixed point is inconsistent with percolation on Potts clusters for q=2, corresponding to the Ising model, and q=3Comment: 11 pages, 3 figures. Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200

Aperiodicity and Disorder - Do They Play a Role?

The effects of an aperiodic order or a random disorder on phase transitions in statistical mechanics are discussed. A heuristic relevance criterion based on scaling arguments as well as specific results for Ising models with random disorder or certain kinds of aperiodic order are reviewed. In particular, this includes an exact real-space renormalization treatment of the Ising quantum chains with coupling constants modulated according to substitution sequences, related to a two-dimensional classical Ising model with layered disorder