Phase transitions in an n-component spin system with a coupling to a non-ordering parameter

Abstract

The renormalization-group method is applied to the analysis of the critical singularities in Gamma _y(q), the correlation function of a non-ordering parameter y. The coupling between y and s, the order parameter with n components, is s²y. When alpha , the specific heat index, is negative, four types of tricritical behaviours are accessible within this Hamiltonian, while the other two may be accessible in other systems in which the non-ordering parameter is a vector. The scaling law gamma _y=(2- eta _y) nu is not only trivially fulfilled (zero identically) between the indices characterizing the leading term of Gamma _y(q), which is a constant, but is also fulfilled between the corrections to scaling, which are the leading singularities when alpha <0, although these are negligible compared with the regular terms.