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Generic phase coexistence in the totally asymmetric kinetic Ising model

Abstract : The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynamics of interfaces and droplets. We revisit the same question for a specific totally asymmetric kinetic Ising model on the square lattice. This nonequilibrium model possesses the remarkable property that its stationary-state measure in the absence of a magnetic field coincides with that of the usual ferromagnetic Ising model. We use both analytical arguments and numerical simulations in order to make progress in the quantitative understanding of the phenomenon of generic phase coexistence. At zero temperature a mapping onto the TASEP allows an exact determination of the time-dependent shape of the ballistic interface sweeping a large square minority droplet of up or down spins. At finite temperature, measuring the mean lifetime of such a droplet allows an accurate measurement of its shrinking velocity $v$, which depends on temperature $T$ and magnetic field $h$. In the absence of a magnetic field, $v$ vanishes with an exponent $\Delta_v\approx2.5\pm0.2$ as the critical temperature $T_c$ is approached. At fixed temperature in the ordered phase, $v$ vanishes at the boundary fields $\pm h_{\rm b}(T)$ which mark the limits of the coexistence region. The boundary fields themselves vanish with an exponent $\Delta_h\approx3.2\pm0.3$ as $T_c$ is approached.
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Contributor : Emmanuelle de Laborderie <>
Submitted on : Thursday, June 8, 2017 - 11:27:12 AM
Last modification on : Monday, June 15, 2020 - 2:52:03 PM
Long-term archiving on: : Saturday, September 9, 2017 - 12:30:46 PM


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  • HAL Id : cea-01534797, version 1
  • ARXIV : 1704.06120



Claude Godrèche, Jean-Marc Luck. Generic phase coexistence in the totally asymmetric kinetic Ising model. 2017. ⟨cea-01534797⟩



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