2014/11/28 by John Golden, Golden, John, Miguel F. Paulos +1 · 1 citation
Computer Science · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.48550/arxiv.1411.7932
v2: minor updates
openalex publication_date 2014/11/28 · arxiv created 2015/01/07 · arxiv updated 2015/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the conformal bootstrap for spacetime dimension 1<d<2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed ε-expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field theories. We also clarify the d→ 1 limit of the conformal bootstrap, showing that bounds can be - and indeed are - discontinuous in this limit. This discontinuity implies that for small ε=d-1 the expected critical exponents for the Ising model are disallowed, and in particular those of the d-1 expansion. Altogether these results strongly suggest that the Ising model universality class cannot be described by a unitary CFT below d=2. We argue this also from a bootstrap perspective, by showing that the 2≤ d<4 Ising "kink" splits into two features which grow apart below d=2.