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The two- and three-dimensional transverse-field Ising models withferromagnetic exchange interactions are analyzed by means of the real-spacerenormalization group method. The basic strategy is a generalization of amethod developed for the one-dimensional case, which exploits the exactinvariance of the model under renormalization and is known to give the exactvalues of the critical point and critical exponent $\nu$. The resulting valuesof the critical exponent $\nu$ in two and three dimensions are in goodagreement with those for the classical Ising model in three and fourdimensions. This is the first example in which a real-space renormalizationgroup on (2+1)- and (3+1)-dimensional Bravais lattices yields accurateestimates of the critical exponents.

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