Global persistence exponent of the two-dimensional Blume-Capel model

Silva, Roberto da; Alves, Nelson A.; Felício, J. R. Drugowich de

doi:10.1103/physreve.67.057102

Cited by 40 publications

(69 citation statements)

References 29 publications

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“…This critical temperature is slightly lower than that reported in Ref. 31, 2.13J / k B . At T c = 2.052J / k B , we compute a dynamic scaling exponent z using the nonequilibrium short-time dynamics of an initial configuration with total magnetization of zero at early times.…”

Section: B Equilibrium Propertiescontrasting

confidence: 48%

“…29 An expanded Bethe-Peierls approximation produced T c = 1.915J / k B , 30 and Monte Carlo simulations suggested that the critical temperature at H = 0 is 1.6950J / k B at D = 0 and 2.1855J / k B at D =5J. 31 In Ref. 31, nonequilibrium short-time dynamics at T c was studied using the heat-bath ͑Glauber͒ transition rate.…”

Section: A Dynamic Propertiesmentioning

confidence: 99%

“…31 In Ref. 31, nonequilibrium short-time dynamics at T c was studied using the heat-bath ͑Glauber͒ transition rate.…”

Section: A Dynamic Propertiesmentioning

confidence: 99%

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Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

Park

2008

Phys. Rev. B

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We consider a S Ն 1 spin model ͑or a generalized Blume-Capel model͒ weakly coupled to a d-dimensional phonon bath and investigate transition rates between different spin configurations. This study is motivated by understanding magnetization relaxation as a function of temperature in diverse magnetic systems such as arrays of magnetic nanoparticles and magnetic molecules. We assume that the magnetization of the spin system relaxes through consecutive emission or absorption of a single phonon. From a weak, linear spin-phonon coupling Hamiltonian, we derive transition rates that would be used to examine dynamic properties of the system in kinetic Monte Carlo simulations. Although the derived phonon-assisted transition rates satisfy detailed balance, in the case of two-and three-dimensional phonon baths, transitions between degenerate states are not allowed. ͑This is a major difference of the phonon-assisted transition rates from the Metropolis and Glauber transition rates.͒ Thus, if there are no alternative paths along which the spin system can relax, the relaxation time diverges. Otherwise, the system finds other paths, which leads to an increase in the relaxation time and energy barrier. However, when higher-order phonon processes are included in the transition rates, it is found that the system can reach the states which were inaccessible due to the forbidden transitions. As a result, the system recovers some of the dynamic properties obtained using the Glauber transition rate.

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Section: B Equilibrium Propertiescontrasting

confidence: 48%

Section: A Dynamic Propertiesmentioning

confidence: 99%

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Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

Park

2008

Phys. Rev. B

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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%

“…The sequence to determine the static exponents from short time dynamics is: first we determine z, performing Monte Carlo simulations that mixes initial conditions [36], and consider the power law for the cumulant…”

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

Self Cite

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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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Exploring the Similarities Between Mean-field and Short-range Relaxation Dynamics of Spin Models

Silva

2022

Braz J Phys

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Global persistence exponent of the two-dimensional Blume-Capel model

Cited by 40 publications

References 29 publications

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

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

Exploring the Similarities Between Mean-field and Short-range Relaxation Dynamics of Spin Models

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