Title: Random Ising model in three dimensions: theory, experiment and simulation - a difficult coexistence
Authors: B.Berche (Groupe M, Laboratoire de Physique des Matériaux, UMR CNRS 7556, Université Henri Poincaré, Nancy 1, F-54506 Vand\oe uvre les Nancy Cedex, France) , P.E.Berche (Groupe de Physique des Matériaux, UMR CNRS 6634, Université de Rouen, F-76801 Saint Etienne du Rouvray Cedex, France) , C.Chatelain (Groupe M, Laboratoire de Physique des Matériaux, UMR CNRS 7556, Université Henri Poincaré, Nancy 1, F-54506 Vand\oe uvre les Nancy Cedex, France) , W.Janke (Institut für Theoretische Physik, Universität Leipzig, D-04109 Leipzig, Germany)

We discuss different approaches to the study of the effect of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalization group calculations provide quite accurate results. Experiments carried out on crystalline mixtures of compounds lead to measurements as accurate as three digits on the values of critical exponents. Numerically, extensive Monte Carlo simulations then pretend to be of comparable accuracy. Life becomes complicated when details are compared between the three approaches.

Key words: random Ising model, renormalization group, Monte Carlo simulations, effective critical exponents
PACS: 05.40.+j, 64.60.Fr, 75.10.Hk