Field-theory results for three-dimensional transitions with complex symmetries

Abstract

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson ${\varphi }^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.

9 pages, Talk at the Conference TH2002, Paris, July 2002

References in corpus (18)

• Critical Phenomena and Renormalization-Group Theory
• Universality of phase transitions of frustrated antiferromagnets
• Critical exponents of the three dimensional diluted Ising model
• Competing orders in a magnetic field: spin and charge order in the cuprate superconductors
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Heisenberg frustrated magnets: a nonperturbative approach
• Randomly dilute spin models: a six-loop field-theoretic study
• Phase transitions in anisotropic superconducting and magnetic systems with vector order parameters: Three-loop renormalization-group analysis
• Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of Dynamical Quarks
• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
• Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering
• Projected SO(5) Models
• Chiral exponents in frustrated spin models with noncollinear ordering
• Randomly dilute spin models with cubic symmetry
• Spin Stiffness of Stacked Triangular Antiferromagnets
• Critical equation of state of randomly dilute Ising systems
• Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)]

Cited by in corpus (10)

• Theory of Intertwined Orders in High Temperature Superconductors
• Ageing Properties of Critical Systems
• On the nature of the finite-temperature transition in QCD
• Five-loop epsilon expansion for U(n)xU(m) models: finite-temperature phase transition in light QCD
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Crossover behavior in three-dimensional dilute spin systems
• Universal behavior of coupled order parameters below three dimensions
• Intertwined Orders and the Physics of High Temperature Superconductors
• Effect of film thickness on the width of percolation threshold in metal-dielectric composites