Critical exponents for structural phase transitions in crystal with defects

Abstract

We find the critical exponents [image omitted]and η as well as α and β, for defect crystal with scalar order parameter in the framework of the renormalization group approach in three dimensions combined with a resummation technique applied to the field theoretical expansions. The problem under consideration may be reduced to analysis of the critical behavior of the n-component hypercubic model with the Hamiltonian [image omitted] in the n→O limit1. The Gell-Mann-Low functions βu(U,V), βv(U,V) and field theoretical expansions for β-1(U,V), β(U,V) have been obtained recently within the three loop approximation2. Our way to resum the two-variable asymptotic series for βU,V and β-1 implies application of the Borel transformation followed by the approximation of the transformed converging series with the socalled Canterbury approximants introduced by Chisholm3, which is a generalisation of the single-variable Pade-Borel method4. More specific, the [2,2/1,1] approximants have been chosen to construct βu, βv an...