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Europhysics Letters (EPL)

Non-equilibrium critical dynamics with domain interface

Nengji Zhou, Bo Zheng

Published May 18, 2007• 11 citations
Publisher

Abstract

With Monte Carlo simulations, we investigate the non-equilibrium critical dynamics with a domain interface, taking the two-dimensional Ising model as an example. Starting from a semi-ordered state, the domain interface grows as time evolves. Dynamic scaling behavior is carefully analyzed. The magnetization and Binder cumulant inside the domain interface are governed by critical exponents different from those outside the domain interface. The ageing phenomenon is identified. For comparison, additional simulations starting from an ordered state have been performed with a free surface and a disordered surface.

DOI
10.1209/0295-5075/78/56001

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With Monte Carlo simulations, we investigate the non-equilibrium critical dynamics with a domain interface, taking the two-dimensional Ising model as an example. Starting from a semi-ordered state, the domain interface grows as time evolves. Dynamic scaling behavior is carefully analyzed. The magnetization and Binder cumulant inside the domain interface are governed by critical exponents different from those outside the domain interface. The ageing phenomenon is identified. For comparison, additional simulations starting from an ordered state have been performed with a free surface and a disordered surface.
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From the non-equilibrium critical relaxation study of the two-dimensional Ising model, the dynamical critical exponent z is estimated to be 2.165 ± 0.010 for this model. The relaxation in the ordered phase of this model is consistent with exp (−√t/τ) behavior. The interface energy of the three-dimensional Ising model is studied and the critical exponent of the correlation length ν and the critical amplitude of the surface tension σ0 are estimated to be 0.6250 ± 0.0025 and 1.42 ± 0.04, respectively. A dynamic Monte Carlo renormalization group method is successfully applied to the equilibrium properties of the three-dimensional Ising model.
We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a method to measure both the dynamic and static critical exponents are reported, based on the finite-size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted independently, while the static exponents \ensuremath{\beta}/\ensuremath{\nu} and \ensuremath{\nu} are obtained from the time evolution of the magnetization and its higher moments. \textcopyright{} 1996 The American Physical Society.