Conformal bootstrap signatures of the tricritical Ising universality class

Abstract

We study the tricritical Ising universality class using conformal bootstrap techniques. By studying bootstrap constraints originating from multiple correlators on the conformal field theory (CFT) data of multiple operator product expansions (OPEs), we are able to determine the scaling dimension of the spin field Δσ in various noninteger dimensions 2≤d≤3. Here, Δσ is connected to the critical exponent η that governs the (tri)critical behavior of the two-point function via the relation η=2-d+2Δσ. Our results for Δσ match with the exactly known values in two and three dimensions and are a conjecture for noninteger dimensions. We also compare our CFT results for Δσ with ϵ-expansion results, available up to ϵ3 order. Our techniques can be naturally extended to study higher-order multicritical points.