Scaling Solutions in Continuous Dimension

TL;DR

This paper investigates the evolution of scaling solutions in the renormalization group flow for the Z_2-effective potential across continuous dimensions, revealing how multi-critical solutions relate to minimal models as dimension approaches two.

Contribution

It introduces a comprehensive analysis of RG flow solutions in continuous dimensions, connecting multi-critical points to minimal models in CFT.

Findings

Multi-critical scaling solutions emerge as dimension decreases from 4.

These solutions converge to unitary minimal models near two dimensions.

The study provides a unified view of critical phenomena across dimensions.

Abstract

We study scaling solutions of the RG flow equation for the Z_2-effective potential in continuous dimension. As the dimension is lowered from d=4 we first observe the appearance of the Ising scaling solution and successively the apparence of multi-critical scaling solutions of arbitrary order. Approaching d=2 these multi-critical scaling solutions converge to the unitary minimal models found in CFT.