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Non-Archimedean Coulomb gases. (English) Zbl 1447.82034

The authors initiate the study of the Coulomb gas model over the \(d\)-dimensional \(p\)-adic space. They establish the existence of equilibrium measures and the \(\Gamma\)-convergence of the Coulomb energy functional when the number of configurations tends to infinity. For a cloud of charged particles confined into the unit ball, they 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. To compare these results with their counterparts for real models see [S. Serfaty, Coulomb gases and Ginzburg-Landau vortices. Zürich: European Mathematical Society (EMS) (2015; Zbl 1335.82002)].

MSC:

82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
11Z05 Miscellaneous applications of number theory

Citations:

Zbl 1335.82002
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References:

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