RG boundaries and interfaces in Ising field theory

TL;DR

This paper studies the boundaries and interfaces formed during renormalization group flows in the 2D Ising model, using numerical methods to classify boundary conditions and analyze complex flows including the Yang-Lee CFT.

Contribution

It provides a comprehensive classification of RG boundary conditions in the 2D Ising model and explores the behavior of RG interfaces, especially in complex magnetic field scenarios.

Findings

RG boundary conditions correspond to regions labeled by UV fixed point boundary conditions.

Numerical techniques reveal the behavior of RG flows, including oscillatory non-convergent interfaces in the Yang-Lee case.

Abstract

Perturbing a CFT by a relevant operator on a half space and letting the perturbation flow to the far infrared we obtain an RG interface between the UV and IR CFTs. If the IR CFT is trivial we obtain an RG boundary condition. The space of massive perturbations thus breaks up into regions labelled by conformal boundary conditions of the UV fixed point. For the 2D critical Ising model perturbed by a generic relevant operator we find the assignment of RG boundary conditions to all flows. We use some analytic results but mostly rely on TCSA and TFFSA numerical techniques. We investigate real as well as imaginary values of the magnetic field and, in particular, the RG trajectory that ends at the Yang-Lee CFT. We argue that the RG interface in the latter case does not approach a single conformal interface but rather exhibits oscillatory non-convergent behaviour.