用图割法计算随机场Potts模型的近似基态
Approximate ground states of the random-field Potts model from graph cuts
摘要：
虽然随机场伊辛模型的基态问题是多项式的，并且可以使用许多用于最大流或图切割的众所周知的算法来解决，但模拟随机场波茨模型对应于已知为NP难的多终端流问题。因此，不太可能存在有效的精确算法。正如我们在这里所展示的，尽管如此，仍然可以使用二进制自由度嵌入到Potts自旋中，并结合图形切割方法来近似地在多项式时间内解决相应的基态问题。我们基准这个启发式算法使用一组准精确的基态发现小系统从长时间并行回火运行。对于不太大数目的$q$的Potts状态，基于图割的方法在一小部分时间内找到相同的解决方案。我们采用新的技术分析了二维随机场Potts模型的破碎长度。
英文摘要：
While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal flow problem that is known to be NP hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasi-exact ground states found for small systems from long parallel tempering runs. For not too large number $q$ of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.
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