Brazilian Journal of Physics

Local persistence and blocking in the two-dimensional blume-capel model

Roberto da Silva, Sílvio R. Dahmen

Published Dec 1, 2004• 7 citations

Abstract

In this paper we study the local persistence of the two-dimensional Blume-Capel Model by extending the concept of Glauber dynamics. We verify that for any value of the ratio alpha = D/J between anisotropy D and exchange J the persistence shows a power law behavior. In particular for alpha < 0 we find a persistence exponent thetal = 0:2096(13), i.e. in the Ising universality class. For alpha > 0 ( a ¹ 1) we observe the occurrence of blocking.

DOI: 10.1590/s0103-97332004000700027

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Brazilian Journal of Physics

Local persistence and blocking in the two-dimensional blume-capel model

Roberto da Silva, Sílvio R. Dahmen

Published Dec 1, 2004• 7 citations

Publisher

Abstract

DOI: 10.1590/s0103-97332004000700027

Related papers

Local persistense and blocking in the two dimensional Blume-Capel Model

Roberto da Silva, Sílvio R. Dahmen

In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio $α=D/J$ between anisotropy $D$ and exchange $J$ the persistence shows a power law behavior. In particular for $α<0$ we find a persistence exponent $θ_{l}=0.2096(13)$ , \textit{i.e.} in the Ising universality class. For $α>0$ ( $α\neq 1$ ) we observe the occurrence of blocking.In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio $α=D/J$ between anisotropy $D$ and exchange $J$ the persistence shows a power law behavior. In particular for $α<0$ we find a persistence exponent $θ_{l}=0.2096(13)$, \textit{i.e.} in the Ising universality class. For $α>0$ ($α\neq 1$) we observe the occurrence of blocking.

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Persistence in Ferromagnetic Ordering: Dependence upon initial configuration

Saikat Chakraborty, Subir K. Das

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions $d=2$ and $3$ . Results for the persistence probability and the domain growth are discussed for quenches to various temperatures ( $T_f$ ) below the critical one ( $T_{c}$ ), from different initial temperatures $T_{i} \geq T_{c}$ . In long time limit, for $T_{i} > T_{c}$ , the persistence probability exhibits power-law decay with exponents $θ\simeq 0.22$ and $\simeq 0.18$ in $d=2$ and $3$ , respectively. For finite $T_i$ , the early time behavior is a different power-law whose life-time diverges and exponent decreases as $T_{i} \rightarrow T_{c}$ . The crossover length between the two steps diverges as the equilibrium correlation length. $T_i=T_c$ is expected to provide a {\it{new universality class}} for which we obtain $θ\simeq 0.035$ in $d=2$ and $\simeq 0.10$ in $d=3$ . The time dependence of the average domain size $\ell$ , however, is observed to be rather insensitive to the choice of $T_i$ .We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions $d=2$ and $3$. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures ($T_f$) below the critical one ($T_{c}$), from different initial temperatures $T_{i} \geq T_{c}$. In long time limit, for $T_{i} > T_{c}$, the persistence probability exhibits power-law decay with exponents $θ\simeq 0.22$ and $\simeq 0.18$ in $d=2$ and $3$, respectively. For finite $T_i$, the early time behavior is a different power-law whose life-time diverges and exponent decreases as $T_{i} \rightarrow T_{c}$. The crossover length between the two steps diverges as the equilibrium correlation length. $T_i=T_c$ is expected to provide a {\it{new universality class}} for which we obtain $θ\simeq 0.035$ in $d=2$ and $\simeq 0.10$ in $d=3$. The time dependence of the average domain size $\ell$, however, is observed to be rather insensitive to the choice of $T_i$.

arXiv:1501.05178Jan 21, 20150 citations

In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio

α=D/J

between anisotropy

D

and exchange

J

the persistence shows a power law behavior. In particular for

α<0

we find a persistence exponent

θ_{l}=0.2096(13)

, \textit{i.e.} in the Ising universality class. For

α>0

(

α\neq 1

) we observe the occurrence of blocking.

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions

d=2

and

3

. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures (

T_f

) below the critical one (

T_{c}

), from different initial temperatures

T_{i} \geq T_{c}

. In long time limit, for

T_{i} > T_{c}

, the persistence probability exhibits power-law decay with exponents

θ\simeq 0.22

and

\simeq 0.18

d=2

and

3

, respectively. For finite

T_i

, the early time behavior is a different power-law whose life-time diverges and exponent decreases as

T_{i} \rightarrow T_{c}

. The crossover length between the two steps diverges as the equilibrium correlation length.

T_i=T_c

is expected to provide a {\it{new universality class}} for which we obtain

θ\simeq 0.035

d=2

and

\simeq 0.10

d=3

. The time dependence of the average domain size

\ell

, however, is observed to be rather insensitive to the choice of

T_i