Wilson's momentum shell renormalization group from Fourier Monte Carlo simulations
Wilson's momentum shell renormalization group from Fourier Monte Carlo simulations
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傅立叶蒙特卡罗模拟中的威尔逊动量壳重整化群
DOI：
10.1016/j.cpc.2010.11.005
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A. Tröster
中科院分区：
文献类型：
--
作者：
A. Tröster
以前从威尔逊的动量壳层重整化公式中精确计算临界指数的尝试，由于存在无限多的无关耦合而受到了困难。以一维长程伊辛模型为例，利用我们最近发展的傅立叶蒙特卡罗算法，模拟计算了不同动量壳层厚度参数b取值时，由耦合常数(u0，r0)所跨越的平面内的动量壳重正化流动。我们报告了在壳层参数bτ<；1附近的不动点耦合和由此产生的指数y⁎<；1的b依赖关系中的强烈反常，它表征了一个薄但有限的动量壳。对该b值的指数的评估产生了其数值精度的显著提高，表明对b=b⁎的无关耦合的影响具有很强的衰减作用。
Previous attempts to accurately compute critical exponents from Wilson's momentum shell renormalization prescription suffered from the difficulties posed by the presence of an infinite number of irrelevant couplings. Taking the example of the 1d long-ranged Ising model, we calculate the momentum shell renormalization flow in the plane spanned by the coupling constants (u0,r0) for different values of the momentum shell thickness parameter b by simulation using our recently developed Fourier Monte Carlo algorithm. We report strong anomalies in the b-dependence of the fixed point couplings and the resulting exponents yτand ω in the vicinity of a shell parameter b⁎<1 characterizing a thin but finite momentum shell. Evaluation of the exponents for this value of b yields a dramatic improvement of their numerical accuracy, indicating a strong damping of the influence of irrelevant couplings for b=b⁎.