Publications (6)3.98 Total impact
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Article: Coarsening of two dimensional XY model with Hamiltonian dynamics: Logarithmically divergent vortex mobility
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ABSTRACT: We investigate the coarsening kinetics of an XY model defined on a square lattice when the underlying dynamics is governed by energy-conserving Hamiltonian equation of motion. We find that the apparent super-diffusive growth of the length scale can be interpreted as the vortex mobility diverging logarithmically in the size of the vortex-antivortex pair, where the time dependence of the characteristic length scale can be fitted as $L(t) \sim ((t+t_{0}) \ln(t+t_{0}))^{1/2}$ with a finite offset time $t_0$. This interpretation is based on a simple phenomenological model of vortex-antivortex annihilation to explain the growth of the coarsening length scale $L(t)$. The nonequilibrium spin autocorrelation function $A(t)$ and the growing length scale $L(t)$ are related by $A(t) \simeq L^{-\lambda}(t)$ with a distinctive exponent of $\lambda \simeq 2.21$ (for $E=0.4$) possibly reflecting the strong effect of propagating spin wave modes. We also investigate the nonequilibrium relaxation (NER) of the system under sudden heating of the system from a perfectly ordered state to the regime of quasi-long-range order, which provides a very accurate estimation of the equilibrium correlation exponent $\eta (E) $ for a given energy $E$. We find that both the equal-time spatial correlation $C_{nr}(r,t)$ and the NER autocorrelation $A_{nr}(t)$ exhibit scaling features consistent with the dynamic exponent of $z_{nr} = 1$.11/2012; -
Article: Double transitions, non-Ising criticality and critical absorbing phase in an interacting monomer-dimer model on a square lattice:
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ABSTRACT: We present a numerical study on an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the $Z_2$ symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We find that the symmetry-breaking transition shows a non-Ising critical behavior, and that the absorbing phase becomes critical, in the sense that the critical decay of the dimer density observed at the absorbing transition persists even within the absorbing phase. Our findings call for further studies on the microscopic models and corresponding continuum description belonging to the generalized voter universality class.03/2011; -
Article: Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling
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ABSTRACT: We investigate, via numerical simulations, the phase ordering kinetics of a two- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible mode cou- pling is included via the conserved conjugate momentum of the spin order parameter (the model E). Coarsening of the system, when quenched from a dis- ordered state to zero temperature, is observed to be enhanced by the existence of the mode coupling terms. The growth of the characteristic length scale L(t) exhibits an effective super-diffusive growth exponent that can be interpreted as a positive logarithmic-like correction to a diffusive growth, i.e., L(t) ~ (t ln t)^{1/2}. In order to understand this behavior, we introduced a simple phenomenological model of coarsening based on the annihilation dynamics of a vortex-antivortex pair, incorporating the effect of vortex inertia and logarithmically divergent mobility of the vortex. With a suitable choice of the parameters, numerical solutions of the simple model can fit the full simulation results very adequately. The effective growth exponent in the early time stage is larger due to the effect of the vortex inertia, which crosses over into late time stage characterized by positive logarithmic correction to a diffusive growth. We also investigated the non-equilibrium autocorrelation function from which the so called {\lambda} exponent can be extracted. We get {\lambda} = 1.99(2) which is distinctively larger than the value of {\lambda} = 1.17 for the purely dissipative model-A dynamics of non-conserved O(2) models.11/2010; -
Article: Coarsening of a nonequilibrium kinetic Ising chain with absorbing transitions: spatial correlation of the order parameters and their dynamic scalings
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ABSTRACT: A one-dimensional nonequilibrium kinetic Ising model possessing two symmetric absorbing states exhibits simultaneous occurrence of two distinct phase transitions, namely the order–disorder transition and the active–absorbing transition. We study the coarsening (both critical and subcritical) process evolving towards the nonequilibrium steady state of this model via the spatial correlations of the order parameters and their dynamic scaling features. For critical coarsening, the length scales associated with the two transitions exhibit the same superdiffusive growth behavior. Critical dynamic scaling behaviors satisfied by the order parameter correlations provide a general relationship between the defect relaxation and the growing length scale. Some of the standard scaling relations between the static critical exponents for the order–disorder transition are found to be modified for the absorbing transition. For subcritical coarsening, the defect correlation exhibits non-monotonic spatial structure due to the interplay between branching and annihilation processes of defects. This structure reveals that, in addition to the usual diffusively growing length scale, there exists a new length scale that grows subdiffusively in time.Journal of Statistical Mechanics Theory and Experiment 08/2010; 2010(08):P08013. · 1.73 Impact Factor -
Article: Nonequilibrium critical relaxations of the order parameter and energy in the two-dimensional ferromagnetic Potts model
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ABSTRACT: The static and dynamic critical properties of the ferromagnetic q-state Potts models on a square lattice with q = 2 and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are investigated, from which static and dynamic critical exponents can be obtained. We find that the static exponents thus obtained from the relaxation of the order parameter and energy together with the second moments of the order parameter exhibit a close agreement with the exact exponents, especially for the case of q = 2 (Ising) model, when care is taken in the choice of the initial states for the relaxation of the second moments. As for the case of q = 3, the estimates for the static exponents become less accurate but still exhibit reasonable agreement with the exactly known static exponents. The dynamic critical exponent for q = 2 (Ising) model is estimated from the relaxation of the second moments of the order parameter with mixed initial conditions to give z(q = 2) = 2.1668(19). Comment: 29 pages, 16 figures08/2008; -
Article: Nonequilibrium critical relaxation of the order parameter and energy in the two-dimensional ferromagnetic Potts model.
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ABSTRACT: The static and dynamic critical properties of the ferromagnetic q -state Potts models on a square lattice with q=2 and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are investigated, from which static and dynamic critical exponents can be obtained. We find that the static exponents thus obtained from the relaxation of the order parameter and energy together with the second moments of the order parameter exhibit a close agreement with the exact exponents, especially for the case of the q=2 (Ising) model, when care is taken in the choice of the initial states for the relaxation of the second moments. As for the case of q=3 , the estimates for the static exponents become less accurate, but still exhibit reasonable agreement with the exactly known static exponents. The dynamic critical exponent for the q=2 (Ising) model is estimated from the relaxation of the second moments of the order parameter with mixed initial conditions to give z(q=2) approximately 2.1668(19) .Physical Review E 05/2008; 77(5 Pt 2):056104. · 2.26 Impact Factor
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Institutions
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2008–2010
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Changwon National University
Changnyeong, South Gyeongsang, South Korea
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