arXiv 0912.28482009-12cond-mat.stat-mechcond-mat.dis-nn

一维Ising类模型中噪声驱动的动态相变

Noise driven dynamic phase transition in a a one dimensional Ising-like model

Parongama Sen

备注：: 4 pages, 5 figures, accepted version in Physical Review E
发表信息：: Phys. Rev E 81 : 032103 (2010)
DOI：: 10.1103/PhysRevE.81.032103

摘要：

最近引入的一维模型\cite{biswas-sen}（以下称为模型I）的动力学演化已经通过引入参数$β$而随机化，使得$β=0$对应于Ising模型，而$β\to \infty$对应于原始模型I。任何$β$值的平衡行为都是相同的：均质状态。我们认为，从动力学指数$z$的行为，对于任何$β\neq 0$，该系统属于动态类模型I表示动态相变在$β= 0$。另一方面，在$L$自旋系统中的持续概率在值$P_{sat}(β, L) = (β/L)^αf(β)$处饱和，其中$α$对于支持在$β=0$处存在动态相变的所有$β\neq 0$保持恒定。缩放函数$f(β)$显示了与用于$β<<1$的$f(β) = \rm{constant} $和用于$β>>1$的$f(β) \propto β^{-α}$的交叉行为。

英文摘要：

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $β$ such that $β=0$ corresponds to the Ising model and $β\to \infty$ to the original model I. The equilibrium behaviour for any value of $β$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $β\neq 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $β= 0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}(β, L) = (β/L)^αf(β)$, where $α$ remains constant for all $β\neq 0$ supporting the existence of the dynamic phase transition at $β=0$. The scaling function $f(β)$ shows a crossover behaviour with $f(β) = \rm{constant} $ for $β<<1$ and $f(β) \propto β^{-α}$ for $β>>1$.

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