Critical behavior of generic competing systems

Abstract

Generic higher character Lifshitz critical behaviors are described using field theory and ${\epsilon }_L$-expansion renormalization group methods. These critical behaviors describe systems with arbitrary competing interactions. We derive the scaling relations and the critical exponents at the two-loop level for anisotropic and isotropic points of arbitrary higher character. The framework is illustrated for the $N$-vector ${\varphi }^4$ model describing a $d$-dimensional system. The anisotropic behaviors are derived in terms of many independent renormalization group transformations, each one characterized by independent correlation lengths. The isotropic behaviors can be understood using only one renormalization group transformation. Feynman diagrams are solved for the anisotropic behaviors using a new dimensional regularization associated to a generalized orthogonal approximation. The isotropic diagrams are treated using this approximation as well as with a new exact technique to compute the integrals. The entire procedure leads to the analytical solution of generic loop order integrals with arbitrary external momenta. The property of universality class reduction is also satisfied when the competing interactions are turned off. We show how the results presented here reduce to the usual $m$-fold Lifshitz critical behaviors for both isotropic and anisotropic criticalities.

RevTex, 54 pages, 3 figures; version accepted for publication in Physical Review B

References in corpus (8)

• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Ghost Inflation
• A unified approach to scaling solutions in a general cosmological background
• Seed perturbations for primordial magnetic fields from MSSM flat directions
• Phantom energy mediates a long-range repulsive force
• Low temperature broken symmetry phases of spiral antiferromagnets
• New universality classes for generic higher character Lifshitz points
• Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors

Cited by in corpus (15)

• Callan-Symanzik-Lifshitz approach to generic competing systems
• Mass Renormalization in Lorentz-violating Scalar Field Theory
• Callan-Symanzik method for $m$-axial Lifshitz points
• Competing interactions and the Lifshitz-type Nonlinear Sigma Model
• Three-loop field renormalization for scalar field theory with Lorentz violation
• Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories
• Critical exponents from parallel plate geometries subject to periodic and antiperiodic boundary conditions
• Critical properties of scalar field theory with Lorentz violation: Exact treatment of Lorentz-violating mechanism
• Susceptibility amplitude ratio for generic competing systems
• Experimental validation of nonextensive statistical field theory: applications to manganites
• Asymptotic single-particle states and exact Lorentz-violating all-loop quantum corrections for scalar field theory
• Is Kaniadakis $\kappa$-generalized statistical mechanics general?
• Is ${\gamma }_{KLS}$-generalized statistical field theory complete?
• Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism
• On the completeness of the ${\delta }_{KLS}$-generalized statistical field theory