零温单自旋翻转动力学中的修正方案
Updating schemes in zero-temperature single-spin flip dynamics
摘要：
在本文中，我们研究了所谓的$c$ -平行更新方案在从无序状态到最终铁磁稳态的弛豫中的作用。本文研究了一维长为$L$的晶格上的两种零温单自旋翻转动力学：流入（即广义零温Glauber动力学）和流出观点动力学.变化的$c$允许我们将更新方案从随机顺序更新（$c=1/L$）改变为确定性同步更新（对于$c=1$）。我们展示了如何平均弛豫时间依赖于$c$和规模与系统大小$L$。此外，我们根据经验找到一个分析公式的流入和流出动态的平均弛豫时间之间的比率。本文的结果表明，在某种意义上说，原来的零温度Glauber动力学是一个关键的一类更广泛的流入动力学。
英文摘要：
In this paper we examine the role of the so called $c$-parallel updating schemes in relaxation from disordered states to the final ferromagnetic steady state. We investigate two zero-temperature single-spin flip dynamics on a one dimensional lattice of length $L$: inflow (i.e. generalized zero-temperature Glauber dynamics) and outflow opinion dynamics. The varying $c$ allows us to change the updating scheme from random sequential updating ($c=1/L$) to deterministic synchronous updating (for $c=1$). We show how the mean relaxation times depend on $c$ and scale with the system size $L$. Moreover, we empirically find an analytical formula for the ratio between mean relaxation times for inflow and outflow dynamics. Results obtained in this paper suggest that in some sense the original zero-temperature Glauber dynamics is a critical one among a broader class of inflow dynamics.
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