Non-Archimedean Coulomb gases
2020; American Institute of Physics; Volume: 61; Issue: 1 Linguagem: Inglês
10.1063/1.5127191
ISSN1527-2427
AutoresW. A. Zúñiga–Galindo, Sergii M. Torba,
Tópico(s)Mathematical Dynamics and Fractals
ResumoThis 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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