Year: 2025
Type: conference-paper
Abstract: The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction of a dual Hamiltonian and a map from the original to the dual observables. By using neural networks to parameterize these maps and introducing a loss function that penalises the difference between correlation functions in original and dual models, we formulate the process of duality discovery as an optimization problem. We numerically solve this problem and show that our framework can rediscover the celebrated Kramers-Wannier duality for the 2d Ising model, numerically reconstructing the known mapping of temperatures. We further investigate the 2d Ising model deformed by a plaquette coupling and find families of ``approximate duals''. We discuss future directions and prospects for discovering new dualities within this framework.
Authors: Gupta, Prateek, Ferrari, Andrea E. V., Iqbal, Nabil
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: International Max Planck Research School for Environmental, Cellular and Molecular Microbiology, Durham University, Humboldt-Universität zu Berlin, Universität Zürich, Freie Universität Berlin, Max-Planck-Institut für Bildungsforschung, Engineering and Physical Sciences Research Council, Science and Technology Facilities Council
OpenAlex ID: W7084301871
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