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

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 $g_s$. We use a combination of analytical and numerical methods to analyze the phase structure of this model as $g_s$ 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.

34 pages + appendices. Many plots and pictures of cubes. Appendix E can be cut out and assembled. Code available at https://github.com/nabiliqbal/3d-ising-string-theory. v2: references added, minor changes

References in corpus (5)

• Generalized Global Symmetries
• "Deconfined" quantum critical points
• Symmetries and Strings in Field Theory and Gravity
• Information geometry in quantum field theory: lessons from simple examples
• Gravity/Spin-model correspondence and holographic superfluids

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• Generalized Symmetries in Condensed Matter
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Exact emergent higher-form symmetries in bosonic lattice models
• Quantum dynamics of topological strings in a frustrated Ising antiferromagnet
• Entanglement entropy from non-equilibrium Monte Carlo simulations
• Interface dynamics in the two-dimensional quantum Ising model
• Baby Universes and Worldline Field Theories
• Magnetisation and mean field theory in the Ising model
• Excitations of Ising Strings on a Lattice
• Dynamics of Quantum Hall Interfaces
• Generalized Landau Paradigm for quantum phases and phase transitions
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories