Extension of scaling to the description of crystals with point defects

Abstract

The concept of scaling is extended to the case of crystals with point defects. In contrast to scaling for defect-free crystals, in order to describe the critical behavior of a crystal with defects, three independent parameters and not two are required. It is shown that the width of the smoothing region is determined by the relation δ ∿ X^α/ν, whereν is the critical exponent describing the temperature dependence of the correlation radius;α is some constant; X is the concentration of point defects. Some new relations are obtained between the critical exponents. These relations are obtained without calling upon the statistical similarity hypothesis.