Critical Behavior of a General O(n)-symmetric Model of two n-Vector Fields in D=4-2 epsilon

TL;DR

This paper investigates the critical behavior of a generalized O(n)-symmetric model with two n-vector fields using renormalization group techniques in a 4-2 epsilon dimensional framework, revealing new fixed points and detailed critical exponents.

Contribution

It introduces a comprehensive analysis of the model's fixed points and critical exponents up to two-loop order, discovering two new fixed points and exploring their properties.

Findings

Found continuous lines of fixed points and O(n)*O(2) invariant solutions.

Identified two new fixed points, one differing at two-loop order from a known fixed point.

Calculated critical exponents eta up to three-loop order.

Abstract

The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed points and critical exponents are calculated up to the one- and two-loop order, resp. (eta in two- and three-loop order). Continuous lines of fixed points and O(n)*O(2) invariant discrete solutions were found. Apart from already known fixed points two new ones were found. One agrees in one-loop order with a known fixed point, but differs from it in two-loop order.