二维和三维伊辛模型的高精度临界点和涨落起源
Critical points with high accuracy and fluctuation origin of 2 and 3-dimensional Ising models
摘要：
本文提出了一种新的普适方法，可显著提高二维和三维伊辛模型临界点的精度，并可探索涨落机制。该方法基于块分形分析和重整化群理论。讨论了自相似变换的层次和重标度规则，定义了有序块的分形维数，其最小值对应于自相似变换的不动点。根据连通性将块划分为不可约块和可约块。发现块自旋有两种态：单态和k重态，每一种态都对应一个系统或一个子系统，该系统或子系统由数学映射建立的块自旋高斯模型描述。利用该模型，我们得到了一个由最小分形维数确定临界点的普适公式。我们计算了三个伊辛模型的临界点，具有很高的精度。这是第一次找到一个临界点只需要一个分形边缘，这导致波动，和点作为波动吸引子。最后，我们讨论了在临界点处不同块自旋的可能性。
英文摘要：
We proposed a new universal method for significantly increasing accuracy of critical points of 2 and 3-dimensional Ising models and exploring fluctuation mechanism. The method is based on analysis of block fractals and the renormalization group theory. We discussed hierarchies and rescaling rule of the self similar transformations, and define a fractal dimension of an ordered block, which minimum corresponds to a fixed point of the transformations. By the connectivity we divide the blocks into two types: irreducible and reducible. We find there are two block spin states: single state and k-fold state, each of which relates to a system or a subsystem described by a block spin Gaussian model set up by mathematic map. Using the model we obtain a universal formula of critical points by the minimal fractal dimensions. We computed the critical points with high accuracy for three Ising models. It is the first time to find a critical point only requires a fractal edge, which causes fluctuations, and the point acts as a fluctuation attractor. Finally, we discussed a possibility of different block spins at the critical point.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
