Critical temperature shifts for layered periodic systems in 1/n expansion

Abstract

A classical n-vector model is considered which is infinitely extended in d-1 dimensions and periodic of period b in the dth dimension. Asymptotically for large values of b the critical temperature is expected to obey a scaling law Tc(b)-Tc( infinity ) approximately Ab- lambda . The authors have calculated the shift exponent lambda to first order in a 1/n expansion for dimensions between three and four. To this order the result is consistent with the assertion lambda = nu d-1 where nu d is the correlation length exponent of the infinitely extended d-dimensional system. From the equivalence between this model and (d-1)-dimensional quantum mechanical systems the behaviour of critical lines near the displacive limit (Tc=0) can be derived.