Real-space renormalization group for the transverse-field Ising model in two and three dimensions

Details Real-space renormalization group for the transverse-field Ising model in two and three dimensions Real-space renormalization group for the transverse-field Ising model in two and three dimensions

2010-12-21

arxiv.org/abs/1012.4557v2

Phys. Rev. E 83, 051103 (2011)

Physics

Condensed Matter

Statistical Mechanics

14 pages, 5 figures, 4 tables

Scientific paper

10.1103/PhysRevE.83.051103

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 $\nu$. The resulting values of the critical exponent $\nu$ in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. 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.

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