Multiple Crossover Phenomena and Scale Hopping in Two Dimensions

TL;DR

This paper investigates the renormalization group flow in a minimal conformal field theory with nearly marginal perturbations, revealing a staircase-like flow, phase transitions, and connections to integrable lattice models.

Contribution

It introduces a novel one-parameter family of hopping trajectories in the RG flow and links these to factorizable scattering theories and phase transitions in conformal field theories.

Findings

Discovery of staircase-like RG flow trajectories.

Identification of phase transitions with multiple fixed points.

Connection between lattice models and different phases of the system.

Abstract

We study the renormalization group for nearly marginal perturbations of a minimal conformal field theory M_p with p >> 1. To leading order in perturbation theory, we find a unique one-parameter family of ``hopping trajectories'' that is characterized by a staircase-like renormalization group flow of the C-function and the anomalous dimensions and that is related to a recently solved factorizable scattering theory. We argue that this system is described by interactions of the form t phi_{(1,3)} - t' \phi_{(3,1)} . As a function of the relevant parameter t, it undergoes a phase transition with new critical exponents simultaneously governed by all fixed points M_p, M_{p-1}, ..., M_3. Integrable lattice models represent different phases of the same integrable system that are distinguished by the sign of the irrelevant parameter t'.