  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.

Statistical Mechanics