Benchmarking the Ising Universality Class in $3 \le d < 4$ dimensions

TL;DR

This paper precisely determines critical exponents of the Ising universality class in dimensions 3 to just below 4 using conformal bootstrap, providing benchmarks and comparing favorably with other methods.

Contribution

It offers highly accurate conformal field theory data for the Ising model across a range of dimensions, advancing previous results and establishing benchmarks.

Findings

Critical exponents determined with 0.1% accuracy

Good agreement with epsilon-expansion, bootstrap, Monte Carlo, and RG methods

Provides detailed dimension-dependent scaling data

Abstract

The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon-expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.