The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

Chen, Y.; Guo, Shuo-Hong; Li, Z.B.; Mǎrculescu, S.; Schülke, L.

doi:10.1007/s100510070060

Cited by 19 publications

(41 citation statements)

References 18 publications

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“…For these reasons, the study of relaxation processes in simple Ising and Potts models with LR interactions plays an important role for the understanding of the dynamics of second-order phase transitions. Within this context, the study of the short-time dynamics (STD) of critical systems has attracted great attention during the last two decades [1,[5][6][7], for a recent review see e.g. [8].…”

Section: Introductionmentioning

confidence: 99%

Study of the nonequilibrium critical quenching and the annealing dynamics for the long-range Ising model in one dimension

2011

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Extensive Monte Carlo simulations are employed in order to study the dynamic critical behaviour of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form 1 r d+σ , with σ = 0.75. The critical temperature, as well as the critical exponents, are evaluated from the power-law behaviour of suitable physical observables when the system is quenched from uncorrelated states, corresponding to infinite temperature, to the critical point. These results are compared with those obtained from the dynamic evolution of the system when it is suddenly annealed at the critical point from the ordered state. Also, the critical temperature in the infinite interaction limit is obtained by means of a finite-range scaling analysis of data measured with different truncated-interaction range. All the estimated static critical exponents (γ/ν, β/ν, and 1/ν ) are in good agreement with Renormalization Group (RG) results and previously reported numerical data obtained under equilibrium conditions. On the other hand, the dynamic exponent of the initial increase of the magnetization (θ) was close to RG predictions. However, the dynamic exponent z of the time correlation length is slightly different than the RG results likely due to the fact that either it may depend on the specific dynamics used or because the two-loop expansion used in the RG analysis may be insufficient.

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Section: Introductionmentioning

confidence: 99%

Study of the nonequilibrium critical quenching and the annealing dynamics for the long-range Ising model in one dimension

2011

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“…Quite a few studies were carried out on models with long-range (LR) interactions. The RG approach of Janssen et al [1] was extended to the case of power-law decaying interactions of the form r −d−σ in the same continuous nvector model [11], in the random Ising model [12], and Send offprint requests to: Katarina Uzelac Correspondence to: katarina@vrabac.ifs.hr in the kinetic spherical model [13,14]. Studies of STD at criticality in discrete models with LR interactions, where such an approach does not apply, are still absent.…”

Section: Introductionmentioning

confidence: 99%

Short-time dynamics in the 1D long-range Potts model

Uzelac¹,

Glumac²,

Barišić³

2008

Eur. Phys. J. B

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We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r 1+σ . The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents θ ′ and z are derived in the cases q = 2 and q = 3 for several values of the parameter σ belonging to the nontrivial critical regime. PACS. 05.50.+q Lattice theory and statistics -05.70.Jk Critical point phenomena -64.60.Ht Dynamic critical phenomena -61.20.Lc Time-dependent properties; relaxation 2 Model and short-time dynamics approach We consider the 1D Potts model defined by the Hamiltonian H = − i 0, s i denotes a q-state Potts spin at the site i, δ is the Kronecker symbol and the summation is over

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“…1,2,3,4,5,6,7,8,9 A thermodynamic system in a critical point is characterized by long-range correlations in equilibrium, so when such a system is quenched from a high temperature T 0 ≫ T c to the critical point T c , the growth of correlations governs the relaxation process. As shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…24, the equilibrium dynamics is also modified and there are two dynamic exponents z ⊥ and z . On the other hand, as the interaction of all order-parameter components with disorder is the same, the susceptibility (as well as the order parameter and heat capacity) is characterized by the single exponent γ and can be written as 23,24,25,26 (6) or in the critical point (τ → 0) as…”

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confidence: 99%

Nonequilibrium critical relaxation in the presence of extended defects

Fedorenko

2004

Phys. Rev. B

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We study nonequilibrium critical relaxation properties of systems with quenched extended defects, correlated in ε d dimensions and randomly distributed in the remaining d − ε d dimensions. Using a field-theoretic renormalization-group approach, we find the scaling behavior of the nonequilibrium response and correlation functions and calculate the initial slip exponents θ and θ ′ , which describe the growth of correlations during the initial stage of the critical relaxation, in the two-loop approximation.

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The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

Cited by 19 publications

References 18 publications

Study of the nonequilibrium critical quenching and the annealing dynamics for the long-range Ising model in one dimension

Study of the nonequilibrium critical quenching and the annealing dynamics for the long-range Ising model in one dimension

Short-time dynamics in the 1D long-range Potts model

Nonequilibrium critical relaxation in the presence of extended defects

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