论文标题
关于随机场Potts模型的优化算法的比较
On the comparison of optimization algorithms for the random-field Potts model
论文作者
论文摘要
对于许多患有猝灭障碍的系统，基础状态的研究可以至关重要地有助于对物理学的彻底理解，如果由零温度的固定点控制或发现有序阶段的特性。尽管可以使用通用优化算法（例如模拟退火或遗传算法）来计算基态，但使用专门针对手头问题专门定制的精确或近似技术通常要高得多。对于某些具有离散自由度的系统，例如随机场Ising模型，有多项式时间方法可以计算精确的基础状态。但是，即使在随机场Potts模型中，状态数量增加了两个以上，问题也变得越来越困难，也无法希望找到相关系统大小的确切基态。在这里，我们比较了此问题的许多近似技术并评估其性能。
For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for uncovering properties of the ordered phase. While ground states can in principle be computed using general-purpose optimization algorithms such as simulated annealing or genetic algorithms, it is often much more efficient to use exact or approximate techniques specifically tailored to the problem at hand. For certain systems with discrete degrees of freedom such as the random-field Ising model, there are polynomial-time methods to compute exact ground states. But even as the number of states increases beyond two as in the random-field Potts model, the problem becomes NP hard and one cannot hope to find exact ground states for relevant system sizes. Here, we compare a number of approximate techniques for this problem and evaluate their performance.
