Functional renormalization group approach to non-collinear magnets

Abstract

A functional renormalization group approach to $d$-dimensional, $N$-component, non-collinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between $d=2.8$ and $d=4$ for various values of $N$ focusing on the critical value $N_c(d)$ that, for a given dimension $d$, separates a first order region for $N<N_c(d)$ from a second order region for $N>N_c(d)$. Our approach concludes to the absence of stable fixed point in the physical - $N=2,3$ and $d=3$ - cases, in agreement with $\epsilon =4-d$-expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on conformal bootstrap program.

16 pages, 8 figures

References in corpus (8)

• Exact evolution equation for the effective potential
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• First order phase transition in the frustrated triangular antiferromagnet CsNiCl3
• Fixed points in frustrated magnets revisited

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