FINITE SIZE SCALING ANALYSIS OF ISING-MODEL BLOCK DISTRIBUTION-FUNCTIONS
FINITE SIZE SCALING ANALYSIS OF ISING-MODEL BLOCK DISTRIBUTION-FUNCTIONS
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DOI：
10.1007/bf01293604
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发表时间：
1981-01-01
期刊：
影响因子：
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通讯作者：
BINDER, K
中科院分区：
文献类型：
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作者：
BINDER, K
对d=2，3，4的Ising格子，研究了线性维有限块中局域序参数的分布函数PL(S)。除了讨论块是无限格子系统的情形外，还讨论了自由[PL(F)(S)]和周期[PL(P)(S)]边界条件下有限系统中的分布。在临界点T_c以上，这些分布趋向于以零块磁化强度为中心的相同的高斯分布，而在T_c以下，这些分布趋向于以±M为中心的两个高斯分布，其中M是无穷大系统中出现的自发磁化强度。然而，在小|S|的分布下，Tc的翅膀明显是非高斯的，反映了两相共存。因此，分布函数可以用来获得有序相之间的界面张力。在临界点，分布函数趋于大的普适形式，尽管依赖于边界条件。这些标度函数是从蒙特卡罗模拟中估计的。作为应用，使用这些分布函数可以从几个方面改进对临界现象的蒙特卡罗研究：(I)序参数、磁化率、界面张力的标准估计得到改进(Ii)T_c可以独立于临界指数估计来估计(Iii)提出了一个类似于Nightingale唯象重整化的蒙特卡罗“重整化群”，它以相当小的工作量得到了相当准确的指数估计(Iv)可以获得关于粗粒哈密顿量的信息，如果将该方法推广到更一般的哈密顿量，这是特别有趣的。
The distribution functionPL(s)of the local order parameters in finite blocks of linear dimensionLis studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is a subsystem of an infinite lattice, also the distribution in finite systems with free [PL(f)(s)] and periodic [PL(p)(s)] boundary conditions is treated. Above the critical pointTc, these distributions tend for largeLtowards the same gaussian distribution centered around zero block magnetization, while belowTcthese distributions tend towards two gaussians centered at ±M, whereMis the spontaneous magnetization appearing in the infinite systems. However, belowTcthe wings of the distribution at small |s| are distinctly nongaussian, reflecting two-phase coexistence. Hence the distribution functions can be used to obtain the interface tension between ordered phases.At criticality, the distribution functions tend for largeLtowards scaled universal forms, though dependent on the boundary conditions. These scaling functions are estimated from Monte Carlo simulations. For subsystem-blocks, good agreement with previous renormalization group work of Bruce is obtained.As an application, it is shown that Monte Carlo studies of critical phenomena can be improved in several ways using these distribution functions:(i)standard estimates of order parameter, susceptibility, interface tension are improved(ii) Tccan be estimated independent of critical exponent estimates(iii)A Monte Carlo “renormalization group” similar to Nightingale's phenomenological renormalization is proposed, which yields fairly accurate exponent estimates with rather moderate effort(iv)Information on coarse-grained hamiltonians can be gained, which is particularly interesting if the method is extended to more general Hamiltonians.