${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization

Abstract

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic (${\mathbb{Z}}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide accurate estimates of the eigenvalue $y_4$ corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from $d=3$ towards $d=2$, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to $O(2)$-symmetric and ${\mathbb{Z}}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.

arXiv comment14 pages, 7 figures

References in corpus (57)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• Functional renormalization group approach to correlated fermion systems
• The nonperturbative functional renormalization group and its applications
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
• Universal Window for Two Dimensional Critical Exponents
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$
• Kosterlitz-Thouless Phase Transition In The Two Dimensional Linear Sigma Model
• Conformal dimensions via large charge expansion
• Supersymmetry and its spontaneous breaking in the random field Ising model
• O(N)-Universality Classes and the Mermin-Wagner Theorem
• Critical exponents of O(N) models in fractional dimensions
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Solving functional flow equations with pseudo-spectral methods
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Infrared behavior in systems with a broken continuous symmetry: classical O(N) model vs interacting bosons
• Randomly dilute Ising model: A nonperturbative approach
• Critical Phenomena in Continuous Dimension
• Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Dimensional crossover of nonrelativistic bosons
• Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase
• Complex networks with tuneable dimensions as a universality playground
• Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Functional renormalization group approach to non-collinear magnets
• Thermodynamics of the two-dimensional XY model from functional renormalization
• A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields
• Finite temperature crossovers near quantum tricritical points in metals
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Critical region of the superfluid transition in the BCS-BEC crossover
• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
• Critical points of coupled vector-Ising systems. Exact results
• Critical Casimir forces from the equation of state of quantum critical systems
• Renormalization-group study of weakly first-order phase transitions
• Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures
• Phase boundary and finite temperature crossovers of the quantum Ising model in two dimensions
• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization

Cited by in corpus (2)

• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group