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The low-temperature specific heat and magnetic susceptibility for dilute concentrations of manganese in copper are studied, using the "statistical model" of Margenau and an expansion of the partition function in a power series of the concentration. An indirect "Ising model" interaction via the conduction electrons is assumed to exist between the magnetic impurities. To find a correction to the statistical model, the two-particle correlation function between impurities is derived in the limit as the temperature approaches zero. It is shown that, in this limit, the system is composed of small clusters of spins that are strongly correlated to each other within a cluster, but various clusters are randomly oriented relative to each other. An impurity within one of these clusters finds itself in an "effective field" arising from the other spins within the cluster and from the random orientation of all spins outside the cluster. This field is a random variable and its probability distribution is easily obtained from the model. The detailed shape of the probability distribution of the field is given for a particular concentration. As the temperature is increased, the internal structure of the clusters is broken up and, at high temperatures, the system exhibits paramagnetic behavior. The theory predicts correctly the experimental low-temperature specific heat and magnetic susceptibility of dilute Cu-Mn.
Klein et al. (Sun,) studied this question.