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

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

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Título Time-dependent Monte Carlo simulations of critical and Lifshitz points of the axial-next-nearest-neighbor Ising model
Autor Silva, Roberto da
Alves Junior, Nelson
Felício, José Roberto Drugovich de
Abstract In this work, we study the critical behavior of second-order points, specifically the Lifshitz point (LP) of a three-dimensional Ising model with axial competing interactions [the axial-next-nearest-neighbor Ising (ANNNI) model], using time-dependent Monte Carlo simulations. We use a recently developed technique that helps us localize the critical temperature corresponding to the best power law for magnetization decay over time: (M)m0=1 ∼ t −β/νz, which is expected of simulations starting from initially ordered states. We obtain original results for the dynamic critical exponent z, evaluated from the behavior of the ratio F2(t ) = (M2) m0=0/ (M)2 m0=1 ∼ t 3/z, along the critical line up to the LP. 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 with 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 that are very different from those of the three-dimensional Ising model (the ANNNI model without the next-nearest-neighbor interactions at the z axis, i.e., J2 = 0), i.e., 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.
Contido em Physical review. E, Statistical, nonlinear, and soft matter physics. Vol. 87, no. 1 (Jan. 2013), 012131, 10 p.
Assunto Magnetizacao
Método de Monte Carlo
Modelo de ising
Pontos criticos
Origem Estrangeiro
Tipo Artigo de periódico
URI http://hdl.handle.net/10183/101845
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