%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