Multicritical behavior in models with two competing order parameters

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.

16 pages, 7 figures, 5 tables, minor changes in updated version, identical to published one in Phys. Rev. E

References in corpus (11)

• Exact evolution equation for the effective potential
• Inflationary Cosmology
• The critical exponents of the superfluid transition in He4
• Ising exponents from the functional renormalisation group
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter
• Critical behavior of the (2+1)-dimensional Thirring model
• Ultracold atoms and the Functional Renormalization Group
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Field theory of bi- and tetracritical points: Statics
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic field

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