On sampling of Monte Carlo data and disordered systems

Abstract

Discusses some arguments concerning the number of experiments required for the Monte Carlo treatment of a disordered system. A theory of large deviations is presented, which is in favour of the usual procedure of taking the arithmetic mean of the experimental data as a reasonable approximation of the exact average. Contrary to a recent suggestion the notion of most probable value does not play any significant role. As an application the authors treat the '+or-J model'. It is argued that in two dimensions this model does not exhibit a phase transition.