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.

Hydrodynamics and transport in the long-range-interacting phi4 chain / Iubini, S.; Lepri, S.; Ruffo, S.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2022:(2022), pp. 1-20. [10.1088/1742-5468/ac59b6]

Hydrodynamics and transport in the long-range-interacting phi4 chain

Lepri, S.
;
Ruffo, S.
2022

Abstract

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.
2022
1
20
033209
https://iopscience.iop.org/article/10.1088/1742-5468/ac59b6
Iubini, S.; Lepri, S.; Ruffo, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/128190
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