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

by Claudio Bonanno, Andrea Cappelli, Mikhail Kompaniets, Satoshi Okuda, Kay Jorge Wiese

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Claudio Bonanno · Andrea Cappelli
Submission information
Preprint Link: scipost_202211_00009v4  (pdf)
Date accepted: 2023-04-03
Date submitted: 2023-03-09 09:34
Submitted by: Bonanno, Claudio
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approaches: Theoretical, Computational


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 $3 \le d < 4$.

Published as SciPost Phys. 14, 135 (2023)

Author comments upon resubmission

``The paper may now be published if the following minor remark would be
addressed: In the new appendix B.2., the relevant parameters for the
resummations are not given for f_{\sigma\sigma\epsilon}. Could you
report the values of a, b_f, \bar b, \bar\lambda and \bar q
that were used to produce the estimates in figure 17?''

In Figs. 17 we used the Self-Consistent resummation method for f_{\sigma \sigma \epsilon} described
in Ref. [41], that does not involve the same optimization of parameters.
At the end of App. B.2, we have added a brief description of
this procedure, as a guide to reading Ref. [41], and compared with
that of Ref. [40] described earlier.

List of changes

Added two paragraphs at the end of Appendix B.2.

Reports on this Submission

Anonymous Report 1 on 2023-3-15 (Invited Report)


The authors have addressed the remaining issues, and the paper may now be published.

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