Struct WilsonianRg 

pub struct WilsonianRg {
    pub d: f64,
    pub epsilon: f64,
    pub lambda: f64,
    pub step: usize,
    pub u: f64,
    pub r: f64,
}

Parameters for a Wilsonian effective field theory in d dimensions.

Implements coarse-graining via momentum-shell integration and block-spin transformation, yielding flow equations for marginal and relevant couplings.

Fields

d: f64

Spacetime dimension d.

epsilon: f64

ε = 4 − d (Wilson-Fisher expansion parameter).

lambda: f64

UV cutoff Λ.

step: usize

Current RG step number (number of coarse-graining steps performed).

u: f64

Coupling u (quartic in φ⁴ theory).

r: f64

Mass parameter r (quadratic coupling).

Implementations

impl WilsonianRg

pub fn new(d: f64, lambda: f64, u: f64, r: f64) -> Self

Construct a Wilsonian RG for φ⁴ theory in d = 4 − ε dimensions.

pub fn step_flow(&mut self, dl: f64, n_components: f64)

Perform one infinitesimal RG step with rescaling factor b = e^{dl}.

One-loop flow equations (ε-expansion): du/dl = ε u − (n+8)/(16π²) u² dr/dl = 2 r + (n+2)/(16π²) u (n = 1 for Ising universality)

pub fn wilson_fisher_fixed_point(&self, n_components: f64) -> f64

Wilson-Fisher fixed point u* for φ⁴ theory (n-component).

u* = (16π² ε) / (n + 8)

pub fn eta_wf(&self, n_components: f64) -> f64

Critical exponent η at Wilson-Fisher fixed point to O(ε²).

η = (n+2) ε² / [2(n+8)²]

pub fn nu_wf(&self, n_components: f64) -> f64

Correlation length exponent ν at Wilson-Fisher fixed point.

1/ν = 2 − (n+2)/(n+8) ε

pub fn rescale_correlation_length(&self, xi: f64, b: f64) -> f64

Block-spin transformation: rescale correlation length by factor b.

Under coarse-graining by b, the correlation length scales as ξ → ξ/b.

pub fn run(&mut self, n_steps: usize, dl: f64, n_components: f64)

Run the RG flow for n_steps steps with step size dl.

Trait Implementations

impl Clone for WilsonianRg

fn clone(&self) -> WilsonianRg

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for WilsonianRg

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.