About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

Understand

We show that the critical behaviour of two- and three-dimensional frustrated magnets cannot reliably be described from the known five- and six-loops perturbative renormalization group results.

• Our conclusions are based on a careful re-analysis of the resummed perturbative series obtained within the zero momentum massive scheme.
• In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order.
• This behaviour strongly suggests that the fixed points found are in fact spurious.