SwissMAP Logo
Log in
  • About us
    • Organization
    • Professors
    • Senior Researchers
    • Postdocs
    • PhD Students
    • Alumni
  • News & Events
    • News
    • Events
    • Online Events
    • Videos
    • Newsletters
    • Press Coverage
    • Perspectives Journal
    • Interviews
  • Research
    • Basic Notions
    • Phase III Directions
    • Phases I & II Projects
    • Publications
    • SwissMAP Research Station
  • Awards, Visitors & Vacancies
    • Awards
    • Innovator Prize
    • Visitors
    • Vacancies
  • Outreach & Education
    • Masterclasses & Doctoral Schools
    • Mathscope
    • Maths Club
    • Athena Project
    • ETH Math Youth Academy
    • SPRING
    • Junior Euler Society
    • General Relativity for High School Students
    • Outreach Resources
    • Exhibitions
    • Previous Programs
    • Events in Outreach
    • News in Outreach
  • Equal Opportunities
    • Mentoring Program
    • Financial Support
    • SwissMAP Scholars
    • Events in Equal Opportunities
    • News in Equal Opportunities
  • Contact
    • Corporate Design
  • Basic Notions
  • Phase III Directions
  • Phases I & II Projects
  • Publications
  • SwissMAP Research Station

A structural test for the conformal invariance of the critical 3d Ising model

Simao Meneses, Slava Rychkov, J. M. Viana Parente Lopes, Pierre Yvernay

7/2/18 Published in : arXiv:1802.02319

How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -- a non-conserved vector operator of dimension exactly (d−1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. We measure the scaling dimension of the lowest virial current candidate V, and find \Delta_V=6\pm1, well above 2 expected for the true virial current. Our result shows that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.

Entire article

Phase I & II research project(s)

  • Field Theory
  • Statistical Mechanics

The law of a point process of Brownian excursions in a domain is determined by the law of its trace

BV equivalence between triadic gravity and BF theory in three dimensions

  • Leading house

  • Co-leading house


The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

© SwissMAP 2025 - All rights reserved