Criticality in the duration of quasistationary state

Antonio Rodríguez, Fernando D. Nobre, and Constantino Tsallis
Phys. Rev. E 104, 014144 – Published 29 July 2021

Abstract

The duration of the quasistationary states (QSSs) emerging in the d-dimensional classical inertial αXY model, i.e., N planar rotators whose interactions decay with the distance rij as 1/rijα (α0), is studied through first-principles molecular dynamics. These QSSs appear along the whole long-range interaction regime (0α/d1), for an average energy per rotator U<Uc (Uc=3/4), and they do not exist for U>Uc. They are characterized by a kinetic temperature TQSS, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature TBG>TQSS. We investigate here the behavior of their duration tQSS when U approaches Uc from below, for large values of N. Contrary to the usual belief that the QSS merely disappears as UUc, we show that its duration goes through a critical phenomenon, namely tQSS(UcU)ξ. Universality is found for the critical exponent ξ5/3 throughout the whole long-range interaction regime.

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  • Received 4 May 2021
  • Accepted 13 July 2021

DOI:https://doi.org/10.1103/PhysRevE.104.014144

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Antonio Rodríguez1, Fernando D. Nobre2, and Constantino Tsallis2,3,4

  • 1GISC, Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros s/n, 28040 Madrid, Spain
  • 2Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
  • 3Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
  • 4Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria

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Issue

Vol. 104, Iss. 1 — July 2021

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