Global fixed point potential approach to frustrated antiferromagnets

TL;DR

This paper uses a nonperturbative renormalization group approach to analyze the critical behavior of frustrated antiferromagnets, providing detailed numerical results for phase transition boundaries.

Contribution

It introduces a functional flow equation method avoiding field expansion artifacts, and computes the critical boundary function N_c(d) for frustrated systems.

Findings

Confirmed previous NPRG results with improved methods

Contradicted fixed dimension perturbative approach

Contradicted some conformal bootstrap results

Abstract

We revisit the critical behavior of classical frustrated systems using the nonperturbative renormalization group (NPRG) equation. Our study is performed within the local potential approximation of this equation to which is added the flow of the field renormalization. Our flow equations are functional to avoid possible artifacts coming from the field expansion of the fixed point potential which consists in keeping only a limited number of coupling constants. We explain in detail our numerical implementation, its advantages and the difficulties encountered in the vicinity of $d=2$. For $N$-component spins, the function $N_c(d)$ separating the regions of first and second order transitions in the $(d,N)$ plane is computed for $d$ between 4 and 2.3. Our results confirm what was previously found with cruder approximations of the NPRG equation and contradict both the fixed dimension perturbative approach and some of the results obtained within the conformal bootstrap approach.