Long-range interactions generated by random Lévy flights: Spin-flip and spin-exchange kinetic Ising model in two dimensions

Huang Jian Xu, Birger Bergersen, Zoltán Rácz

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A d=2 dimensional kinetic Ising model that evolves by a combination of spin flips and spin exchanges is investigated. The spin flips satisfy detailed balance for the equilibrium state of the Ising model at temperature T while the spin exchanges are random Lévy flights of dimension σ=1.5. Our Monte Carlo (MC) simulations show that the steady state of this system displays a second-order phase transition as T is lowered. Comparing the critical fluctuations of the magnetization to those of an Ising model in which the interaction decays with distance as r-3.5, we find that, within the resolution of the MC data, the critical exponents and the scaling functions of the two systems coincide. We argue that this coincidence indicates that a recent conjecture about the random Lévy flights generating long-range interaction of the form Veff(r)∼r-d-σ is valid not only in the spherical limit and in d=1 but also in d=2.

Original languageEnglish
Pages (from-to)1520-1524
Number of pages5
JournalPhysical Review E
Issue number3
Publication statusPublished - Jan 1 1993


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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