无向有向Barabási-Albert网络和Erdös-Rényi随机图上$Q$ -态Potts模型零温动力学的持久性
Persistence in the zero-temperature dynamics of the $Q$-states Potts model on undirected-directed Barabási-Albert networks and Erdös-Rényi random graphs
摘要：
本文利用零温Glauber动力学研究了Potts模型中的持续概率$P(t)$，其中$Q=3,4,5,7,9,12,24,64, 128$，$256, 512, 1024,4096,16384 $，. {\it有向}和{ \it无向} Barabási-Albert网络和Erdös-Rényi随机图上的$2^{30}$状态.在这个模型中，我们发现对于{ \it无向}和{ \it有向} Erdös-Rényi随机图，$P(t)$在短时间内指数衰减到零.对于{ \it定向}和{ \it无向} Barabási-Albert网络，相反，它在很长一段时间内以指数方式衰减到一个恒定值，即对于所有来自$Q=3,4,5,..., 2^{30}$的$Q$值（本文研究），$P(\infty)$都不为零;这表明所有这些$Q$值都是“阻塞”的。除了在{ \it无向}情况下的$Q=2^{30}$，$P(t)$以指数方式趋向于零;这可能只是一个有限大小的效应，因为在其他“阻塞”情况下，你可能只有几个不变的自旋。
英文摘要：
The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {\it directed} and {\it undirected} Barabási-Albert networks and Erdös-Rényi random graphs. In this model it is found that $P(t)$ decays exponentially to zero in short times for {\it directed} and {\it undirected} Erdös-Rényi random graphs. For {\it directed} and {\it undirected} Barabási-Albert networks, in contrast it decays exponentially to a constant value for long times, i.e, $P(\infty)$ is different from zero for all $Q$ values (here studied) from $Q=3,4,5,..., 2^{30}$; this shows "blocking" for all these $Q$ values. Except that for $Q=2^{30}$ in the {\it undirected} case $P(t)$ tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
