Wang-Landau算法在格点规范理论中的应用
Applying the Wang-Landau Algorithm to Lattice Gauge Theory
摘要：
我们在SU（N）格点规范理论的背景下实现了Wang-Landau算法。我们研究了淬火的、简化的晶格理论，并计算了N= 20，30，40，50时的态密度。我们介绍了一个变种的原始算法中使用的权重函数的更新不渐近线到一个固定的功能，而是继续有小的波动，提高隧道。我们制定了一种方法来评估的状态密度的错误，并使用的结果来计算的平均作用密度和比热的依赖性的`t Hooft耦合λ。这使我们能够定位耦合λ_t，在该耦合处，系统中发生强烈的一阶跃迁。对于N=20和30，我们将我们的结果与使用Ferrenberg-Swendsen多重直方图重新加权获得的结果进行比较，发现误差为0.2%或更小。将我们的结果外推到N=oo，我们发现1/lambda_t = 0.3148（2）。我们注意到这一结果对于SU（N）格点规范理论的猝灭大$N$约化的有效性的意义。
英文摘要：
We implement the Wang-Landau algorithm in the context of SU(N) lattice gauge theories. We study the quenched, reduced version of the lattice theory and calculate its density of states for N=20,30,40,50. We introduce a variant of the original algorithm in which the weight function used in the update does not asymptote to a fixed function, but rather continues to have small fluctuations which enhance tunneling. We formulate a method to evaluate the errors in the density of states, and use the result to calculate the dependence of the average action density and the specific heat on the `t Hooft coupling lambda. This allows us to locate the coupling lambda_t at which a strongly first order transition occurs in the system. For N=20 and 30 we compare our results to those obtained using Ferrenberg-Swendsen multi-histogram reweighting and find agreement with errors of 0.2 % or less. Extrapolating our results to N=oo we find 1/lambda_t = 0.3148(2). We remark on the significance of this result for the validity of quenched large-$N$ reduction of SU(N) lattice gauge theories.
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