格子气变量下伊辛模型的重整化群映射
Renormalization group maps for Ising models in lattice gas variables
摘要：
实空间重整化群映射，例如，多数规则变换，将Ising型模型映射到更粗格上的Ising型模型。我们表明，在格子气变量的重整化哈密顿量的每个系数只依赖于有限数量的值的重整化哈密顿量。我们介绍了一种方法，它计算的重整化哈密顿量的值与高精度，从而计算系数的格子气变量与高精度。对于具有择多规则变换的正方格点上的临界最近邻伊辛模型，我们计算了重整化哈密顿量的格子气变量表示中1,000多个不同的系数，并研究了这些系数的衰减。我们发现它们在某种意义上呈指数衰减，但衰减速率很慢。我们还表明，自旋变量中的系数是敏感的截断方法来计算它们。
英文摘要：
Real space renormalization group maps, e.g., the majority rule transformation, map Ising type models to Ising type models on a coarser lattice. We show that each coefficient of the renormalized Hamiltonian in the lattice gas variables depends on only a finite number of values of the renormalized Hamiltonian. We introduce a method which computes the values of the renormalized Hamiltonian with high accuracy and so computes the coefficients in the lattice gas variables with high accuracy. For the critical nearest neighbor Ising model on the square lattice with the majority rule transformation, we compute over 1,000 different coefficients in the lattice gas variable representation of the renormalized Hamiltonian and study the decay of these coefficients. We find that they decay exponentially in some sense but with a slow decay rate. We also show that the coefficients in the spin variables are sensitive to the truncation method used to compute them.
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