1996/05/17 by Muyu Guo, R. N. Bhatt, David A. Huse · 4 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed matter physics #Curse of dimensionality #Gravitational singularity #Ising model #Lattice (music) #Magnetic susceptibility #Mathematics #Mean field theory #Paramagnetism #Physics #Quantum many-body systems #Quantum mechanics #Statistics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevb.54.3336
published as Phys. Rev. B 54, 3336-3342 (1996) · 20 pages, REVTEX, 6 eps figures included using the epsf macros; to appear in Phys. Rev. B
arxiv created 1996/05/17 · openalex publication_date 1996/08/01 · arxiv updated 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We report a Monte Carlo study of the effects of fluctuations in the bond distribution of Ising spin glasses in a transverse magnetic field, in the paramagnetic phase in the T\ensuremath→0 limit. Rare, strong fluctuations give rise to Griffiths singularities, which can dominate the zero-temperature behavior of these quantum systems, as originally demonstrated by McCoy for one-dimensional (d=1) systems. Our simulations are done on a square lattice in d=2 and a cubic lattice in d=3, for a Gaussian distribution of nearest neighbor (only) bonds. In d=2, where the linear susceptibility was found to diverge at the critical transverse field strength \mathrm\ensuremathΓc for the order-disorder phase transition at T=0, the average nonlinear susceptibility \mathrm\ensuremathχnl diverges in the paramagnetic phase for \ensuremathΓ well above \mathrm\ensuremathΓc, as is also demonstrated in the accompanying paper by Rieger and Young. In d=3, the linear susceptibility remains finite at \mathrm\ensuremathΓc, and while Griffiths singularity effects are certainly observable in the paramagnetic phase, the nonlinear susceptibility appears to diverge only rather close to \mathrm\ensuremathΓc. These results show that Griffiths singularities remain persistent in dimensions above one (where they are known to be strong), though their magnitude decreases monotonically with increasing dimensionality (there being no Griffiths singularities in the limit of infinite dimensionality). \textcopyright 1996 The American Physical Society.