Non-Factorizing Interface in the Two-Dimensional Long-Range Ising Model

TL;DR

This paper investigates a two-dimensional long-range Ising model with a line defect, demonstrating that it does not factorize into two halves in the infrared limit, challenging the factorization proposal in conformal field theories.

Contribution

It provides a perturbative analysis showing non-factorization in a long-range Ising model with a defect, offering an intuitive higher-dimensional explanation.

Findings

The long-range Ising model at criticality does not factorize across a defect.

Factorization fails even in the infrared limit in the perturbative regime.

The model's equivalence to a higher-dimensional CFT explains the non-factorization.

Abstract

The factorization proposal claims that the co-dimension one "pinning defect", on which a local relevant operator is integrated, factorizes the space into two halves in general conformal field theories in the infrared limit. In this letter, we study a two-dimensional long-range Ising model at criticality with a line defect or an interface, which physically corresponds to changing the local temperature on it. We show that in the perturbative regime, it is not factorizing even in the infrared limit. An intuitive explanation of the non-factorization is that the long-range Ising model is equivalent to a local conformal field theory in higher dimensions. In this picture, the space is still connected through the "extra dimension" across the defect line.