Miyazaki Ryoji, Nishimori Hidetoshi, Ortiz Gerardo
Department of Physics, Tokyo Institute of Technology, Megro-ku, Tokyo, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051103. doi: 10.1103/PhysRevE.83.051103. Epub 2011 May 2.
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.
利用实空间重整化群方法分析了具有铁磁交换相互作用的二维和三维横向场伊辛模型。基本策略是对为一维情况开发的方法进行推广，该方法利用了重整化下模型的精确不变性，并且已知能给出临界点和临界指数ν的精确值。二维和三维中临界指数ν的所得值与三维和四维经典伊辛模型的结果吻合良好。据我们所知，这是第一个在（2 + 1）维和（3 + 1）维布拉维晶格上的实空间重整化群能准确估计临界指数的例子。
