Boundary Criticality at the Nishimori Multicritical Point

TL;DR

This paper investigates boundary critical phenomena at the Nishimori multicritical point in a 2D random-bond Ising model using tensor-network methods, revealing conformal boundary fixed points and multifractal boundary spin behavior.

Contribution

It introduces a tensor-network approach to analyze boundary criticality at the Nishimori point, identifying conformal boundary fixed points and connecting numerical results with RG analysis.

Findings

Identified two conformal boundary fixed points: free and fixed boundaries.

Extracted conformal data such as boundary entropies and scaling dimensions.

Discovered multifractal scaling of boundary spin fields at the free boundary fixed point.

Abstract

We study boundary critical behavior at the Nishimori multicritical point of the two-dimensional (2D) random-bond Ising model. Using tensor-network methods, we realize a one-parameter family of microscopic boundary conditions by continuously rotating the boundary-spin orientation and find two conformal boundary fixed points that correspond to the free and fixed boundaries. We extract conformal data, including the boundary entropies and the scaling dimensions of boundary primary operators, which characterize the boundary universality class. We further demonstrate that the free boundary fixed point exhibits multifractal scaling of boundary spin fields. Finally, we complement our numerical results with a renormalization group analysis and discuss a systematic bridge between the controlled $6-\epsilon$ expansion and the 2D tensor network numerics.