Random Ising model in three dimensions: theory, experiment and simulation - a difficult coexistence

Bertrand Berche, Pierre-Emmanuel Berche, Christophe Chatelain, Wolfhard Janke

Published 2004-11-10, updated 2004-12-03Version 2

We discuss different approaches for studying the influence of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalisation 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.