Randomly dilute spin models with cubic symmetry

Abstract

We study the combined effect of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. For this purpose, we consider the field-theoretical approach based on the Ginzburg-Landau-Wilson ${\varphi }^4$ Hamiltonian with cubic-symmetric quartic interactions and quenched randomness coupled to the local energy density. We compute the renormalization-group functions to six loops in the fixed-dimension (d=3) perturbative scheme. The analysis of such high-order series provides an accurate description of the renormalization-group flow. The results are also used to determine the critical behavior of three-dimensional antiferromagnetic three- and four-state Potts models in the presence of quenched impurities.

23 pages, 1 figures

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• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• Cubic fixed point in three dimensions: Monte Carlo simulations of the ${\varphi }^4$ model on the lattice
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• Platonic Field Theories
• Fixed points in frustrated magnets revisited
• Spin models with random anisotropy and reflection symmetry
• Field-theory results for three-dimensional transitions with complex symmetries
• Six dimensional Landau-Ginzburg-Wilson theory
• Infinite distances in multicritical CFTs and higher-spin holography
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
• Towards a fully automated computation of RG-functions for the 3-$d$ O(N) vector model: Parametrizing amplitudes
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Cubic* criticality emerging from a quantum loop model on triangular lattice
• Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• The Cubic Fixed Point at Large $N$