Ising model in a boundary magnetic field with random discontinuities

TL;DR

This paper studies a 2D Ising model with a boundary magnetic field that has random discontinuities, analyzing boundary conditions, RG flows, and integrability aspects in a boundary field theory framework.

Contribution

It introduces a boundary field theory model with random boundary magnetic fields, deriving exact reflection matrices and analyzing RG flows and fixed points.

Findings

Exact reflection matrix derived for the model

Boundary entropy calculated and RG flow space analyzed

Model exhibits multiple infrared fixed points and potential breakdown of integrability

Abstract

We consider a two-dimensional Ising field theory on a space with boundary in the presence of a piecewise constant boundary magnetic field which is allowed to change value discontinuously along the boundary. We assume zero magnetic field in the bulk. The positions of discontinuities are averaged over as in the annealed disorder. This model is described by a boundary field theory in which a superposition of the free spin boundary condition is perturbed by a collection of boundary condition changing operators. The corresponding boundary couplings give the allowed constant values of the magnetic field as well as the fugacities for the transitions between them. We show that when the value of the magnetic field is allowed to take only two different values which are the same in magnitude but have different signs the model can be described by a quadratic Lagrangian. We calculate and analyse the exact reflection matrix for this model. We also calculate the boundary entropy and study in detail the space of RG flows in a three-parameter space and with four different infrared fixed points. We discuss the likely breakdown of integrability in the extended model which allows for two generic values of the boundary magnetic field, backing it by some calculations.