A two-dimensional Kurganov-Tadmor finite-volume scheme accurately solves FRG flow equations for effective potentials in multi-dimensional field space, benchmarked against exact zero-dimensional path integrals and applied to 3D O(2) and O(N)xO(M) models.
Global fixed point potential approach to frustrated antiferromagnets
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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.
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Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
A two-dimensional Kurganov-Tadmor finite-volume scheme accurately solves FRG flow equations for effective potentials in multi-dimensional field space, benchmarked against exact zero-dimensional path integrals and applied to 3D O(2) and O(N)xO(M) models.