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On fourpoint connectivities in the critical 2d Potts model
by Marco Picco, Sylvain Ribault, Raoul Santachiara
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Sylvain Ribault · Raoul Santachiara 
Submission information  

Preprint Link:  https://arxiv.org/abs/1906.02566v2 (pdf) 
Date accepted:  20190919 
Date submitted:  20190828 02:00 
Submitted by:  Ribault, Sylvain 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We perform MonteCarlo computations of fourpoint cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to fourpoint functions in a CFT that interpolates between Dseries minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT fourpoint functions, down to the $2$ to $4$ significant digits of our MonteCarlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the halfplane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.
Author comments upon resubmission
List of changes
Answer to the Anonymous Report 2:
1. In order to clarify this point, we have modified the beginning of Section 3.3 by using the word 'analytic' rather than 'exact' for the coefficients of the relation, and by adding the clause 'while stressing that the relation cannot be exact' at the end of the first paragraph.
2. At the end of Section 3.3, we have written dependences on Q explicitly.
3. For the basic equation (1.2), we have given [8] as a reference.
4. It is true that the structure constants of the odd CFT Eq. (2.16) are related to structure constants of Liouville theory. However, the relation is not simple or straightforward. Before and after (2.16), we have added references to the article [13], which specifically discusses the relation, rather than to works on Liouville theory.
5. We have cited the recommended DelfinoViti article (now [6]) in Section 1.1, and added the sentence 'In particular, the threepoint connectivity of the twodimensional Potts model was found to be related to a threepoint function in Liouville theory [6]'.
Answer to the Anonymous Report 1:
1. We have added clickable links to the specific versions of the cited articles that we have used in the two cases where they were missing. We disagree that journal references are needed to identify cited articles: using a search engine, titles are enough. Moreover, titles provide more useful information to the reader than journal references.
2. We have added captions to the figures and tables that did not have any. (Except a few small tables which are better treated as equations.)
3. We have added labels to the axes of the figures that did not have any.
4. There is no summary of the main results at the end of the paper because there is already a section 'introduction and summary' at the beginning.
5. We have corrected the typo 'a fourpoint functions encodes' on page 2. On the other hand, 'phenomenons' is a nonstandard but correct plural form of 'phenomenon'.
Further modifications:
We have added the reference [33] in Section A.1.
Published as SciPost Phys. 7, 044 (2019)
Reports on this Submission
Report
The authors have made the appropriate changes in the revised version of their manuscript. This is an interesting paper that contributes to understanding CFT as applied to these models. I recommend publication of the manuscript in its present form.
Anonymous on 20190903 [id 587]
Editorial comment on item 1 in reply to anonymous report 1:
Indeed, titles are very helpful and SciPost is encouraging the inclusion of titles (see https://scipost.org/submissions/author_guidelines for the guidelines ). Beyond this, the authors are free to have their opinion, but they should still respect the standards of SciPost, in particular they should not create unnecessary work for a journal that is operating free of cost. Consequently, the authors will be expected to submit a version with all the required information (in particular the DOI for all references where one is available) prior to publication.