Machine learning and optimization-based approaches to duality in statistical physics

• URL: http://arxiv.org/abs/2411.04838v1
• Date: Thu, 07 Nov 2024 16:29:03 GMT
• Title: Machine learning and optimization-based approaches to duality in statistical physics
• Authors: Andrea E. V. Ferrari, Prateek Gupta, Nabil Iqbal,
• Abstract summary: duality is the idea that a given physical system can have two different mathematical descriptions. We numerically solve the problem and show that our framework can rediscover the celebrated Kramers-Wannier duality for the 2d Ising model. We also discuss an alternative approach which uses known features of the mapping of topological lines to reduce the problem to optimize the couplings in a dual Hamiltonian.
• Score: 2.3727769223905515
• License:
• 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 simple 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, reconstructing the known mapping of temperatures. We also discuss an alternative approach which uses known features of the mapping of topological lines to reduce the problem to optimizing the couplings in a dual Hamiltonian, and explore next-to-nearest neighbour deformations of the 2d Ising duality. We discuss future directions and prospects for discovering new dualities within this framework.

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