Toward a 3d Ising model with a weakly-coupled string theory dual

Iqbal, Nabil; McGreevy, John

Abstract

It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. The usual Ising Hamiltonian measures the area of these domain walls. This theory has string coupling of unit magnitude. We add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling gs. We use a combination of analytical and numerical methods to analyze the phase structure of this model as gs is varied. We study statistical properties of the topology of worldsheets and discuss the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.

Citation

Iqbal, N., & McGreevy, J. (2020). Toward a 3d Ising model with a weakly-coupled string theory dual. SciPost Physics, 9(2), Article 019. https://doi.org/10.21468/scipostphys.9.2.019

• Journal Article Type: Article
• Acceptance Date: Aug 10, 2020
• Online Publication Date: Aug 13, 2020
• Publication Date: 2020
• Deposit Date: Aug 13, 2020
• Publicly Available Date: Aug 23, 2020
• Journal: SciPost Physics.
• Print ISSN: 2542-4653
• Electronic ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 2
• Article Number: 019
• DOI: https://doi.org/10.21468/scipostphys.9.2.019
• Public URL: https://durham-repository.worktribe.com/output/1258521
• Related Public URLs: https://arxiv.org/abs/2003.04349