Critical structure factors of bilinear fields in O(N)-vector models

Abstract

We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum behavior of the corresponding scaling functions, and give general interpolation formulae based on a dispersive approach. Moreover, we determine the crossover exponent $\phi_T$ associated with the traceless tensorial quadratic field, by computing and analyzing its six-loop perturbative expansion in fixed dimension. We find: $\phi_T=1.184(12)$, $\phi_T=1.271(21)$, and $\phi_T=1.40(4)$ for $N=2,3,5$ respectively.