Conformal invariance in the long-range Ising model

Paulos, M.F.; Rychkov, S.; van Rees, B.C.; Zan, B.

Abstract

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Citation

Paulos, M., Rychkov, S., van Rees, B., & Zan, B. (2016). Conformal invariance in the long-range Ising model. Nuclear Physics B, 902, 246-291. https://doi.org/10.1016/j.nuclphysb.2015.10.018

• Journal Article Type: Article
• Acceptance Date: Oct 28, 2015
• Online Publication Date: Nov 29, 2015
• Publication Date: Jan 1, 2016
• Deposit Date: Dec 30, 2015
• Publicly Available Date: Jan 25, 2016
• Journal: Nuclear Physics B
• Print ISSN: 0550-3213
• Electronic ISSN: 1873-1562
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 902
• Pages: 246-291
• DOI: https://doi.org/10.1016/j.nuclphysb.2015.10.018
• Public URL: https://durham-repository.worktribe.com/output/1424355
• Related Public URLs: http://arxiv.org/abs/1509.00008