Statistical Models with a Line of Defect

TL;DR

This paper analyzes integrable models with a defect line, deriving reflection-transmission equations, and explicitly computes amplitudes for the Ising model involving Majorana fermions, revealing key scattering features.

Contribution

It derives reflection-transmission equations for integrable models with a defect and explicitly solves them for the Ising model with Majorana fermions.

Findings

Solutions only exist for S = ±1 in diagonal S-matrix cases.

Transmission and reflection amplitudes are explicitly computed for the Ising model.

The S = -1 case corresponds to the Ising model with Majorana fermions.

Abstract

The factorization condition for the scattering amplitudes of an integrable model with a line of defect gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal $S$-matrix in the bulk are only those with $S =\pm 1$. The choice $S=-1$ corresponds to the Ising model. We compute the transmission and reflection amplitudes relative to the interaction of the Majorana fermion with the defect and we discuss their relevant features.