CNR ExploRA

Articolo in rivista, 2022, ENG, 10.1088/1742-5468/ac59b6

Hydrodynamics and transport in the long-range-interacting phi (4) chain

Iubini, Stefano; Lepri, Stefano; Ruffo, Stefano

Consiglio Nazionale Delle Ricerche, Istituto Dei Sistemi Complessi, Via Madonna del Piano 10, Sesto Fiorentino, I-50019, Italy; Istituto Nazionale Di Fisica Nucleare, Sezione Di Firenze, Via G. Sansone 1, Sesto Fiorentino, I-50019, Italy; Sissa And INFN, Sezione Di Trieste, Via Bonomea 265, Trieste, I-34136, Italy

We present a simulation study of the one-dimensional phi (4) lattice theory with long-range interactions decaying as an inverse power r (-(1+sigma)) of the intersite distance r, sigma > 0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0 < sigma <= 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for sigma > 1 and anomalous for 0 < sigma < 1, where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Levy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.

Journal of statistical mechanics 2022 (3), pp. 033209-1–033209-20