%0 Journal Article %T Block Renormalization for quantum Ising models in dimension $d=2$ : applications to the pure and random ferromagnet, and to the spin-glass %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %A Monthus, Cécile %Z v2=final version (21 pages, 6 figures) %< avec comité de lecture %Z t15/090 %@ 1742-5468 %J Journal of Statistical Mechanics: Theory and Experiment %I IOP Publishing %V 2015 %N 01 %P 023 %8 2015-01-19 %D 2015 %Z 1409.8459 %R 10.1088/1742-5468/2015/01/P01023 %Z Physics [physics]Journal articles %X For the quantum Ising chain, the self-dual block renormalization procedure of Fernandez-Pacheco [Phys. Rev. D 19, 3173 (1979)] is known to reproduce exactly the location of the zero-temperature critical point and the correlation length exponent $\nu=1$. Recently, Miyazaki and Nishimori [Phys. Rev. E 87, 032154 (2013)] have proposed to study the disordered quantum Ising model in dimensions $d>1$ by applying the Fernandez-Pacheco procedure successively in each direction. To avoid the inequivalence of directions of their approach, we propose here an alternative procedure where the $d$ directions are treated on the same footing. For the pure model, this leads to the correlation length exponents $\nu \simeq 0.625$ in $d=2$ (to be compared with the 3D classical Ising model exponent $\nu \simeq 0.63$) and $\nu \simeq 0.5018$ (to be compared with the 4D classical Ising model mean-field exponent $\nu =1/2$). For the disordered model in dimension $d=2$, either ferromagnetic or spin-glass, the numerical application of the renormalization rules to samples of linear size $L=4096$ yields that the transition is governed by an Infinite Disorder Fixed Point, with the activated exponent $\psi \simeq 0.65$, the typical correlation exponent $\nu_{typ} \simeq 0.44$ and the finite-size correlation exponent $\nu_{FS} \simeq 1.25$. We discuss the similarities and differences with the Strong Disorder Renormalization results. %G English %2 https://cea.hal.science/cea-01322782/document %2 https://cea.hal.science/cea-01322782/file/1409.8459v2.pdf %L cea-01322782 %U https://cea.hal.science/cea-01322782 %~ CEA %~ CNRS %~ DSM-IPHT %~ CEA-UPSAY %~ UNIV-PARIS-SACLAY %~ CEA-UPSAY-SACLAY %~ CEA-DRF %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE