Hinczewski Michael, Berker A Nihat
Feza Gürsey Research Institute, TUBITAK-Bosphorus University, Cengelköy 34684, Istanbul, Turkey.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1 Pt 1):011104. doi: 10.1103/PhysRevE.77.011104. Epub 2008 Jan 7.
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10(-5) along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows.
最近发展起来的张量重整化群（TRG）方法为推导晶格哈密顿量的热力学和临界性质提供了一种高精度技术。TRG是一种局部粗粒化变换，每个晶格点处张量的元素起着经历重整化群流的相互作用的作用。这些张量流与无限系统的相图结构直接相关，每个相流向不同的不动点表面。沿流的不动点分析和求和给出了临界指数以及整个温度范围内的热力学函数。因此，对于铁磁三角晶格伊辛模型，在整个温度范围内计算出的自由能精度优于10^(-5)。与以前的位置空间重整化群方法不同，这种通用方法中的（张量指标范围D的）截断在直接且系统的改进下收敛。我们使用D = 24很容易得到最佳结果，这对应于4624维的重整化群流。
