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.
Multicritical behavior in models with two competing order parameters
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abstract
We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N_1, N_2 plane. We study the fate of non-trivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of non-canonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.
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cond-mat.stat-mech 1years
2024 1verdicts
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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.