cea-01322782
https://cea.hal.science/cea-01322782
https://cea.hal.science/cea-01322782/document
https://cea.hal.science/cea-01322782/file/1409.8459v2.pdf
arxiv:1409.8459
doi:10.1088/1742-5468/2015/01/P01023
[CEA] CEA - Commissariat à l'énergie atomique
[CNRS] CNRS - Centre national de la recherche scientifique
[DSM-IPHT] IPHT
[CEA-UPSAY] CEA - Université Paris-Saclay
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[CEA-UPSAY-SACLAY] CEA-UPSAY-SACLAY
[CEA-DRF] Direction de Recherche Fondamentale
[GS-MATHEMATIQUES] Graduate School Mathématiques
[GS-PHYSIQUE] Graduate School Physique
Block Renormalization for quantum Ising models in dimension $d=2$ : applications to the pure and random ferromagnet, and to the spin-glass
Monthus, Cécile
[PHYS] Physics [physics]
ART
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.
2015-01-19
2016-05-27
en
Journal of Statistical Mechanics: Theory and Experiment
IOP Publishing