Dimensional Reduction by Conformal Bootstrap

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.

23 page, 13 figures

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• Rigorous bounds on irrelevant operators in the 3d Ising model CFT
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• The fate of Parisi-Sourlas supersymmetry in Random Field models
• Improving the five-point bootstrap
• Ising model close to $d=2$
• Finite-size scaling of the random-field Ising model above the upper critical dimension
• Is there supersymmetric Lee-Yang fixed point in three dimensions?
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Factorized lightcone expansion of conformal blocks
• On the breakdown of dimensional reduction and supersymmetry in random-field models