Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents

Originality
+ 4 - 0
Accuracy
+ 3 - 0
Score
7.59
4707 views
Referee this paper: arXiv:1403.4545 by S. El-Showk, M.F. Paulos, D. Poland, (show more)

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

(Is this your paper?)


This 2014 paper by S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi  uses ''the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several $Z_2$-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension $\Delta_\sigma=0.518154(15)$, and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.''

summarized by Arnold Neumaier , Dilaton
paper authored Mar 17, 2014 to cond-mat by  (no author on PO assigned yet) 
  • [ revision history ]
    edited Aug 31, 2014 by Arnold Neumaier

    I found this very positive commentary by L. Kadanoff.

    I found this talk given by David Simmons-Duffin (one of the authors) at KITP on the subject. 

    Perhaps we can ask Kadanoff to import his text as a review?

    Here is a quora answer by David Simons-Duffin on how to read the two papers. 

    1 Review

    + 3 like - 0 dislike

    The 3-dimensional Ising model is a highly important model field theory because many realistic thermodynamic systems - among them all real fluids - are believed to belong to the universality class of this model. (See, e.g., the discussion and references in my paper here.)

    The paper under review is an excellent paper, using the relations between conformal field theory and field theories at critical points and newly developed theoretical tools (a variant of the bootstrap program) to calculate the critical exponents of the 3-dimensional Ising model to an accuracy significantly exceeding the previously best calculations (which were obtained by Monte Carlo methods). This shows that the theoretical methods of operator-based quantum field theory are now developed to a very high level.

    The techniques are also applied to the 2-dimensional Ising model, which is exactly solvable, with similarly good numerical results.

    I already reviewed  a companion paper which contains the theoretical results underlying the present paper. I will complete this review in due time by describing the numerical methods, why they work, and what sort of results are obtained. (But because of traveling I must pause for more than week; so be patient.) 

    reviewed Sep 16, 2014 by Arnold Neumaier (15,787 points) [ revision history ]
    edited Sep 20, 2014 by Arnold Neumaier
    looking forward to your review. This should really motivate me to start reading some OPE and CFT stuff.

    Your Review:

    Please use reviews only to (at least partly) review submissions. To comment, discuss, or ask for clarification, leave a comment instead.
    To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
    Please consult the FAQ for as to how to format your post.
    This is the review box; if you want to write a comment instead, please use the 'add comment' button.
    Live preview (may slow down editor)   Preview
    Your name to display (optional):
    Privacy: Your email address will only be used for sending these notifications.
    Anti-spam verification:
    If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
    p$\hbar$ysicsOve$\varnothing$flow
    Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
    Please complete the anti-spam verification




    user contributions licensed under cc by-sa 3.0 with attribution required

    Your rights
    ...