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We develop a novel real-space renormalization group (RG) scheme whichaccurately estimates correlation length exponent $\nu$ near criticality ofhigher-dimensional quantum Ising and Potts models in a transverse field. Ourmethod is remarkably simple (often analytical), grouping only a few spins intoa block spin so that renormalized Hamiltonian has a closed form. A previousdifficulty of spatial anisotropy and unwanted terms is avoided by incorporatingrotational invariance and internal $\mathbb{Z}_q$ symmetries of theHamiltonian. By applying this scheme to the (2+1)-dim Ising model on atriangular lattice and solving an analytical RG equation, we obtain $\nu\approx0.6300$. This value is within statistical errors of the current bestMonte-Carlo result, 25th-order high-temperature series expansions,$\phi^4$-theory estimation which considers up to seven-loop corrections andexperiments performed in low-Earth orbits. We also apply the scheme tohigher-dimensional Potts models for which ordinary Monte-Carlo methods are noteffective due to strong hysteresis and suppression of quantum fluctuation in aweak first-order phase transition.

Precise estimation of critical exponents from real-space renormalization group analysis