Random matrices theory elucidates the nonequilibrium critical phenomena

Roberto da Silva ()
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Roberto da Silva: Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 05, 1-10

Abstract: The earlier times of the evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices built from different time evolutions of a simple testbed spin system, as the spin-1/2 and spin-1 Ising models, we analyzed the density of eigenvalues for different temperatures of the so called Wishart matrices. We observe a transition in the shape of the distribution that presents a gap of eigenvalues for temperatures lower than the critical temperature, or in its roundness, with a continuous migration to the Marchenko–Pastur law in the paramagnetic phase. We consider the analysis a promising method to be applied in other spin systems, with or without defined Hamiltonian, to characterize phase transitions. Our approach differs from the alternatives in literature since it uses the concept of magnetization matrix, not the spatial matrix of single spins.

Keywords: Random matrices; Time-dependent Monte Carlo simulations; Phase transitions and critical phenomena; Marchenko–Pastur law (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123500614

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