Critical Phenomena in Continuous Dimension

Abstract

We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents nu(d) and eta(d) both from a lowest--order and a complete first--order derivative expansion of the effective average action. In particular, this can be used to study critical behavior as a function of dimensionality at fixed temperature.

5 pages, 1 figure, PLB version, references added

References in corpus (11)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Optimised Renormalisation Group Flows
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Precise determination of critical exponents and equation of state by field theory methods
• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$
• Effective average action in statistical physics and quantum field theory
• The Renormalization Group and Two Dimensional Multicritical Effective Scalar Field Theory
• The effectiveness of the local potential approximation in the Wegner-Houghton renormalization group
• A non perturbative approach of the principal chiral model between two and four dimensions

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• An Introduction to the Nonperturbative Renormalization Group
• Fundamentals of the Exact Renormalization Group
• Ising exponents from the functional renormalisation group
• A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
• Non-perturbative Approach to Critical Dynamics
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model
• 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
• Scaling Solutions in Continuous Dimension
• Criticality of the random field Ising model in and out of equilibrium: a nonperturbative functional renormalization group description
• Renormalization group for phases with broken discrete symmetry near quantum critical points
• A note on scaling arguments in the effective average action formalism
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
• Critical Behavior and Dimension Crossover of Pion Superfluidity
• Renormalized phi^6 model for quantum phase transitions in systems of itinerant fermions
• Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
• Critical Casimir forces for O(N) models from functional renormalization
• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Phase boundary and finite temperature crossovers of the quantum Ising model in two dimensions
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Quantum interface unbinding transitions
• Capillary-wave models and the effective average action scheme of functional renormalization group
• Approximating the Ising model on fractal lattices of dimension below two
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models