Scaling solutions in the derivative expansion

Abstract

Scalar field theories with ${\mathbb{Z}}_2$-symmetry are the traditional playground of critical phenomena. In this work these models are studied using functional renormalization group (FRG) equations at order ${\partial }^2$ of the derivative expansion and, differently from previous approaches, the spike plot technique is employed to find the relative scaling solutions in two and three dimensions. The anomalous dimension of the first few universality classes in $d=2$ is given and the phase structure predicted by conformal field theory is recovered (without the imposition of conformal invariance), while in $d=3$ a refined view of the standard Wilson-Fisher fixed point is found. Our study enlightens the strength of shooting techniques in studying FRG equations, suggesting them as candidates to investigate strongly non-perturbative theories even in more complex cases.

16 pages, 5 figures

References in corpus (17)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Ising exponents from the functional renormalisation group
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Critical exponents of O(N) models in fractional dimensions
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Scaling Solutions in Continuous Dimension
• Lee-Yang model from the functional renormalization group
• Leading CFT constraints on multi-critical models in d>2
• Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings
• Anisotropic Long-Range Spin Systems
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• New universality class in three dimensions: The critical Blume-Capel model
• Are there scaling solutions in the O(N)-models for large N in d>4?
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Functional RG approach to the Potts model
• Multicritical points of the O(N) scalar theory in $2<d<4$ for large N

Cited by in corpus (13)

• The nonperturbative functional renormalization group and its applications
• Criticality of Spin Systems with Weak Long-Range Interactions
• Essential renormalisation group
• Complex networks with tuneable dimensions as a universality playground
• Functional Renormalization and $\overline{\text{MS}}$
• Topological phase transitions in four dimensions
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• Renormalization-Group Running Induced Cosmic Inflation
• Non-perturbative quantum Galileon in the exact renormalization group
• Nonperturbative treatment of a quenched Langevin field theory
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Higher-derivative four-dimensional sine-Gordon model