Short-Time Dynamic Exponents of an Ising Model With Competing Interactions

Alves, Neri; Felício, J. R. Drugowich de

doi:10.1142/s0217984903005068

Cited by 10 publications

(6 citation statements)

References 24 publications

(44 reference statements)

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“…The theoretical predictions (T ) of β l /ν and θ l are also included [102]. Non-universality was also observed in the Ising model with competing first-and second-neighbour interactions [111][112][113]. The Hamiltonian is…”

Section: Disorder Effectsmentioning

confidence: 99%

Study of phase transitions from short-time non-equilibrium behaviour

Albano¹,

Bab²,

Baglietto³

et al. 2011

Rep. Prog. Phys.

113

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We review recent progress in the understanding of phase transitions and critical phenomena, obtained by means of numerical simulations of the early dynamic evolution of systems prepared at well-specified initial conditions. This field has seen exhaustive scientific research during the last decade, when the renormalization-group (RG) theoretical results obtained at the end of the 1980s were applied to the interpretation of dynamic Monte Carlo simulation results. While the original RG theory is restricted to critical phenomena under equilibrium conditions, numerical simulations have been applied to the study of far-from-equilibrium systems and irreversible phase transitions, the investigation of the behaviour of spinodal points close to first-order phase transitions and the understanding of the early-time evolution of self-organized criticality (SOC) systems when released far form the SOC regime. The present review intends to provide a comprehensive overview of recent applications in those fields, which can give the flavour of the main ideas, methods and results, and to discuss the directions for further studies. All of these numerical results pose new and interesting theoretical challenges that remain as open questions to be addressed by new research in the coming years.

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Section: Disorder Effectsmentioning

confidence: 99%

Study of phase transitions from short-time non-equilibrium behaviour

Albano¹,

Bab²,

Baglietto³

et al. 2011

Rep. Prog. Phys.

113

View full text Add to dashboard Cite

show abstract

“…Another critical exponent found only in the nonequilibrium state is the exponent θ that characterizes the anomalous behavior of the order parameter in the shorttime regime. Formerly, a positive value was always associated to this exponent [4,8,34,35,36,37,38] and the phenomenon was known as critical initial slip. However, some models can exhibit negative values for the exponent θ.…”

Section: B the Dynamic Critical Exponent θmentioning

confidence: 99%

“…where d is the dimension of the system. This approach proved to be very efficient in estimating the exponent z for a great number of models [5,7,8,19,38,42]. In this technique, for different lattice sizes, the double-log curves of F 2 versus t fall on the same straight line, without any rescaling of time, resulting in more precise estimates for z.…”

Section: The Dynamic Critical Exponent Zmentioning

confidence: 99%

An alternative order parameter for the 4-state potts model

Fernandes

Arashiro

Felício

et al. 2006

Physica A: Statistical Mechanics and its Applications

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We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A: Math. Gen. 20, L549 (1987)] in the study of the Z(5) model. We have estimated the global persistence exponent θg by following the time evolution of the probability P (t) that the considered order parameter does not change its sign up to time t. We have also obtained the critical exponents θ, z, ν, and β using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.

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“…Using Monte Carlo simulations, many authors have obtained the dynamic exponents θ and z as well as the static ones β and ν, and other specific exponents for several models: Baxter-Wu [35], 2, 3 and 4-state Potts [36,37], Ising with multispin interactions [38], Ising with competing interactions [39], models with no defined Hamiltonian (celular automata) [40], models with tricritical point [41], Heisenberg [42], protein folding [43] and so on.…”

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 Dynamic Exponents of an Ising Model With Competing Interactions

Cited by 10 publications

References 24 publications

Study of phase transitions from short-time non-equilibrium behaviour

Study of phase transitions from short-time non-equilibrium behaviour

An alternative order parameter for the 4-state potts model

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

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