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

Iqbal, Nabil and McGreevy, John (2020) 'Toward a 3d Ising model with a weakly-coupled string theory dual.', SciPost physics., 9 (2). 019.


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.

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Publisher statement:Copyright N. Iqbal and J. McGreevy. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
Date accepted:10 August 2020
Date deposited:23 August 2020
Date of first online publication:13 August 2020
Date first made open access:23 August 2020

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