Read the equation
Each component loses φgᵢ² and receives γ times the total squared coupling magnitude. Summing across components gives (nγ−φ)Σgⱼ², which shows how dimension affects the total drift. The subsequent FixedPoint helper only iterates this flow a fixed number of times and does not verify that the derivative has reached zero.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| g_i | Coupling component |
| phi | Golden ratio |
| gamma | Declared shared coefficient |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
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Original context
Read the surrounding source passage
return result
}
// BetaFunction computes the beta function for golden couplings
func BetaFunction(g []float64) []float64 {
beta := make([]float64, len(g))
for i := range beta {
// β_i = -φ·g_i² + γ·Σ_j g_j² (simplified)
sum := 0.0
for _, gj := range g {
sum += gj * gj
}
beta[i] = -PHI*g[i]*g[i] + GAMMA*sum
}
return beta
}
// FixedPoint finds fixed point of RG flowExact original notation
β_i = -φ·g_i² + γ·Σ_j g_j² (simplified)