Dimensional Reduction by Conformal Bootstrap

TL;DR

This paper uses conformal bootstrap methods to analyze dimensional reductions in branched polymers and RFIM, confirming validity in certain dimensions and identifying deviations below five dimensions.

Contribution

It applies conformal bootstrap techniques to evaluate scale dimensions, providing new insights into the validity of dimensional reduction in specific models and dimensions.

Findings

Dimensional reduction holds for 3 ≤ D ≤ 8 in branched polymers.

Deviations from dimensional reduction appear below five dimensions in RFIM.

Results align with D'=D-2 dimensional Yang-Lee and Ising models.

Abstract

The dimensional reductions in the branched polymer and the random field Ising model (RFIM) are discussed by a conformal bootstrap method. The small size minors are applied for the evaluations of the scale dimensions of these two models and the results are compared to D'=D-2 dimensional Yang-Lee edge singularity and to pure D'=D-2 dimensional Ising model, respectively. For the former case, the dimensional reduction is shown to be valid for $3 \le D \le 8$, and for the latter case, the deviation from the dimensional reduction can be seen below five dimensions.