Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries

We present a numerical study of two-dimensional random-bond Ports ferromagn ets. The model is studied both below and above the critical value Q(c)=4, w hich discriminates between second- and first-order transitions in the pure system. Two geometries are considered, namely cylinders and Square-shaped s ystems, and the critical behavior is investigated through conformal invaria nce techniques that were recently shown to be valid, even in the randomness -induced second-order phase transition:regime Q>4. In the cylinder geometry , connectivity transfer matrix calculations provide a simple test to find t he range of disorder amplitudes that is characteristic of the disordered fi xed point. The scaling dimensions then follow from the exponential decay of correlations along the strip. Monte Carlo simulations of spin systems on t he other hand are generally performed on systems of rectangular shape on th e square lattice, but the data are then perturbed by strong surface effects . The conformal mapping of a semi-infinite system inside a square enables u s to take into account boundary effects explicitly and leads to an accurate determination of the scaling dimensions. The techniques are applied to dif ferent values of Q in the range 3-64. [S1063-651X(99)19010-X].