Monte Carlo Simulations of Short-Time Critical Dynamics

Zheng, Bo

doi:10.1142/s021797929800288x

Cited by 276 publications

(412 citation statements)

References 86 publications

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“…For large L, at the critical point τ = 0, and for m 0 ≪ 1, from the scaling form given by equation (2) one derives the initial increase in magnetization, obtaining [18,19] …”

Section: Short-time Dynamics Approach For Critical Phenomenamentioning

confidence: 99%

“…θ and x 0 are the exponents of the initial increase and the scaling dimension of the order parameter. Since both exponents are related, one of them can be considered as a new no trivial critical exponent [18,19]. Performing simulations for different values of the initial magnetization and extrapolating the results to m 0 = 0, the exponent θ can be obtained.…”

Section: Short-time Dynamics Approach For Critical Phenomenamentioning

confidence: 99%

“…a completely ordered one and a completely disordered one, is sufficient to determine both the critical temperature and the set of relevant critical exponents in a self-consistent fashion [18,19,20].…”

Section: Short-time Dynamics Approach For Critical Phenomenamentioning

confidence: 99%

“…Finally, the dynamic exponent z was evaluated, for first time for this fractal, by means of two independent methods using the Binder's cumulant and the critical scaling of time correlation functions. The STD approach has shown to be a powerful tool in the study of critical phenomena because the critical exponents can be determined before the critical slowing down of the dynamics takes place and they are free from finite size corrections, provided that the correlation length ξ(t) is always smaller than the system size L (ξ(t) ≪ L) [18,19]. However, in the case that we are interested in, namely the SC(3,1), an intrinsic kind of finite-size effects due to the segmentation step k of the fractal can be observed, as it is discussed in details below.…”

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confidence: 99%

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Critical behavior of an Ising system on the Sierpinski carpet: A short-time dynamics study

2005

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The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent θ of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent θ exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent z shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.

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“…For large L, at the critical point τ = 0, and for m 0 ≪ 1, from the scaling form given by equation (2) one derives the initial increase in magnetization, obtaining [18,19] …”

Section: Short-time Dynamics Approach For Critical Phenomenamentioning

confidence: 99%

Section: Short-time Dynamics Approach For Critical Phenomenamentioning

confidence: 99%

Section: Short-time Dynamics Approach For Critical Phenomenamentioning

confidence: 99%

mentioning

confidence: 99%

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Critical behavior of an Ising system on the Sierpinski carpet: A short-time dynamics study

2005

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“…We present our alternative derivation of some power laws in the short time dynamics context. Readers, who want a more complete review about this topic, may want to read [32,33].…”

Section: B Non-equilibrium Critical Dynamicsmentioning

confidence: 99%

Time-dependent Monte Carlo simulations of critical and Lifshitz points of the axial-next-nearest-neighbor Ising model

2013

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In this work, we study the critical behavior of second order points and specifically of the Lifshitz point (LP) of a three-dimensional Ising model with axial competing interactions (ANNNI model), using time-dependent Monte Carlo simulations. First of all, we used a recently developed technique that helps us localize the critical temperature corresponding to the best power law for magnetization decay over time: M m 0 =1 ∼ t −β/νz which is expected of simulations starting from initially ordered states. Secondly, we obtain original results for the dynamic critical exponent z, evaluated from the behavior of the ratio F2(t) = M 2 m 0 =0 / M 2 m 0 =1 ∼ t 3/z , along the critical line up to the LP. Finally, we explore all the critical exponents of the LP in detail, including the dynamic critical exponent θ that characterizes the initial slip of magnetization and the global persistence exponent θg associated to the probability P (t) that magnetization keeps its signal up to time t. Our estimates for the dynamic critical exponents at the Lifshitz point are z = 2.34(2) and θg = 0.336(4), values very different from the 3D Ising model (ANNNI model without the next-nearest-neighbor interactions at z-axis, i.e., J2 = 0) z ≈ 2.07 and θg ≈ 0.38. We also present estimates for the static critical exponents β and ν, obtained from extended time-dependent scaling relations. Our results for static exponents are in good agreement with previous works

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Short-Time Critical Behavior of Systems with Random Impurities

Chen¹,

Guo²,

Li³

2001

phys. stat. sol. (b)

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The theoretical renormalization-group approach is applied to the study of the short-time critical behavior of the Ginzburg-Landau model with long-range random impurities which have a power-like correlation r ÀðdÀqÞ . The system initially at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with a model A dynamics. The asymptotic scaling laws are studied in the frame of a double expansion in E ¼ 4 À d and d ¼ E þ q with d of the order of E. The initial slip exponent q 0 for the order parameter is calculated up to the first order in E ¼ 4 À d or in E 1=2 corresponding to different fixed points, respectively. For d < 4, the short-time behavior of the order parameter is investigated in one loop. Two different logarithmic and exponential-logarithmic corrections to short-time behaviors of both the autocorrelation and the order parameter are also solved in d ¼ 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n ¼ 4 (where n is the spin dimensionality) in d ¼ 4 dimension.

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Monte Carlo Simulations of Short-Time Critical Dynamics

Cited by 276 publications

References 86 publications

Critical behavior of an Ising system on the Sierpinski carpet: A short-time dynamics study

Critical behavior of an Ising system on the Sierpinski carpet: A short-time dynamics study

Time-dependent Monte Carlo simulations of critical and Lifshitz points of the axial-next-nearest-neighbor Ising model

Short-Time Critical Behavior of Systems with Random Impurities

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