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  • Open Access

Nonfactorizing interface in the two-dimensional long-range Ising model

Dongsheng Ge*

Yu Nakayama†

  • *Contact author: dge@het.phys.sci.osaka-u.ac.jp
  • †Contact author: yu.nakayama@yukawa.kyoto-u.ac.jp
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Phys. Rev. D 113, 065028 – Published 26 March, 2026

DOI: https://doi.org/10.1103/blrz-phyn

Abstract

The factorization proposal claims that the codimension 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 paper, 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 nonfactorization 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.

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Phys. Rev. D 113, 065028– Published 26 March, 2026
  • Received 21 July 2025
  • Accepted 27 February 2026
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