Critical behavior of frustrated systems: Monte Carlo simulations versus renormalization group

Abstract

We study the critical behavior of frustrated systems by means of the Padé-Borel resummed three-loop renormalization group expansions and numerical Monte Carlo simulations. Amazingly, for six-component spins, where the transition is second-order, both approaches disagree. This unusual situation is analyzed both from the point of view of the convergence of the resummed series and from the possible relevance of nonperturbative effects.