On correlation functions in random magnets

In random magnets the probability distribution of the correlation function at large distance is not concentrated around its average. To illustrate this idea two examples are studied: a random Ising chain and a random cubic chain. The extension of the findings to higher dimension and the connection to Harris' criterion (1974) are discussed heuristically. It is concluded that in Monte Carlo simulations due to the combined effects of randomness and finite size effects one can only measure the most probable value of the correlation functions and not their average.