Module renormalization_group

Expand description

Renormalization group (RG) theory computations.

This module implements the modern apparatus of the renormalization group:

Beta functions: one-loop and two-loop beta functions, UV/IR fixed points
RG flow: Callan-Symanzik equation, running coupling, anomalous dimensions
Wilsonian RG: effective field theory, block-spin / coarse-graining transformations
Universality classes: Ising, XY, Heisenberg, mean-field critical exponents
Scaling relations: hyperscaling, Rushbrooke, Josephson, Fisher identities
Renormalization schemes: MS-bar, momentum subtraction, on-shell
Operator product expansion: OPE coefficients, conformal blocks, fusion rules
Critical phenomena: correlation length, order parameter, susceptibility
Decimation transformation: 1-D Ising decimation, block-spin flow equations
Conformal field theory: central charge, scaling dimensions, partition function

Structs§

BetaFunction: Beta function for a single running coupling constant g.
ConformalFieldTheory: Conformal field theory (CFT) data for a 2-D critical theory.
CriticalExponents: Set of universal critical exponents for a given universality class.
CriticalPhenomena: Critical phenomena observables near a second-order phase transition.
DecimationTransformation: 1-D Ising decimation RG transformation.
OpeCoefficient: OPE coefficient C_{ijk} for operators O_i × O_j → O_k.
OperatorProductExpansion: Operator product expansion registry.
RenormalizedCoupling: Scheme-dependent renormalized coupling and counterterms.
RgFlow: Callan-Symanzik RG flow for coupling and mass.
RgFlowResult: Result of integrating the Callan-Symanzik RG flow equations.
ScalingRelations: Verification of thermodynamic scaling relations from critical exponents.
WilsonianRg: Parameters for a Wilsonian effective field theory in d dimensions.

LoopOrder: Loop order for beta-function computation.
RenormalizationScheme: Renormalization scheme for field theory calculations.
UniversalityClass: Universality class of a critical point.