Non-Archimedean Coulomb gases

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Abstract

This article aims to study the Coulomb gas model over the d-dimensional p-adic space. We establish the existence of equilibrium measures and the Γ-limit for the Coulomb energy functional when the number of configurations tends to infinity. For a cloud of charged particles confined into the unit ball, we compute the equilibrium measure and the minimum of its Coulomb energy functional. The p-adic Coulomb energy is the continuum limit of the minus a hierarchical Hamiltonian attached to a spin glass model with a p-adic coupling.

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Zúñiga-Galindo, W. A., & Torba, S. M. (2020). Non-Archimedean Coulomb gases. Journal of Mathematical Physics, 61(1). https://doi.org/10.1063/1.5127191

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