Overrelaxation algorithms for lattice field theories.
Overrelaxation algorithms for lattice field theories.
复制标题
格场论的过松弛算法。
DOI：
10.1103/physrevd.37.458
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
Adler
中科院分区：
文献类型：
--
作者：
Adler
我们研究超松弛算法热化的格场理论与多二次和更一般的行动。超松弛算法是满足详细平衡条件的热浴算法的单参数推广;参数是松弛参数。欧米加0... 0（极端欠松弛）极限的超松弛算法是等价的朗之万方程的方法。我们分析了自由场作用的热化，并表明，对于...欧米茄..一个超松弛的高斯-赛德尔算法产生一个临界的慢下来，这是独立的波长，并有一个相关的时间，这是一个因子N小于一个未加速的雅可比迭代，与N的线性尺寸的晶格在晶格单位。对于一般的非多二次作用，我们给出了一个广义超松弛算法，它满足详细的平衡，关于一个有效的行动，这是明确可计算的原始行动。在SU（n）格点规范理论的情况下，我们用这种构造来表示一个超松弛算法，它具有精确的格点规范不变性，并且满足关于有效作用量的详细平衡，该有效作用量与Wilson作用量的区别仅在于连续极限中的相对更高阶a/sup 2/，具有格点间距a。«少
We study overrelaxation algorithms for the thermalization of lattice field theories with multiquadratic and more general actions. Overrelaxation algorithms are one-parameter generalizations of the heat-bath algorithm which satisfy the detailed-balance condition; the parameter is the relaxation parameter ..omega.., 0 ..0 (extreme underrelaxation) limit of the overrelaxation algorithm is equivalent to the Langevin equation approach. We analyze the thermalization of a free-field action, and show that for ..omega..approx.2 an overrelaxed Gauss-Seidel algorithm yields a critical slowing down which is independent of wavelength, and has a correlation time which is a factor N smaller than that for an unaccelerated Jacobi iteration, with N the linear dimension of the lattice in lattice units. For a general nonmultiquadratic action, we give a generalized overrelaxation algorithm which satisfies detailed balance with respect to an effective action which is explicitly computable in terms of the original action. In the case of SU(n) lattice gauge theory we use this construction to formulate an overrelaxed algorithm which has exact lattice gauge invariance, and which satisfies detailed balance with respect to an effective action differing from the Wilson action only by terms of relativemore » order a/sup 2/ in the continuum limit, with a the lattice spacing.« less