On the critical behaviour of the Ising model with impurities-existence of anomalous logarithmic terms

In order to discuss critical behaviours of impure systems, in particular the concentration-dependence of critical exponents, anomalous logarithmic terms are investigated up to the first order of the concentration from the viewpoint of the unrenormalized expansion theory of critical exponents. It is shown that there appear such anomalous logarithmic terms in the first-order expansion when the specific heat in the corresponding pure system diverges logarithmically. It is thus pointed out that there is a possibility that critical exponents may vary as the concentration changes.