Unconventional critical activated scaling of two-dimensional quantum spin glasses

Abstract

We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with two different short-range bond distributions, the bimodal and the Gaussian ones. Through an exhaustive finite-size analysis, we show that the cumulant probably follows an unconventional activated scaling, which we interpret as new evidence supporting the hypothesis that the quantum critical behavior is governed by an infinite randomness fixed point. PACS numbers: 75.10.Nr, 64.70.Tg, 75.40.Mg, 75.50.Lk Quantum phase transitions in condensed matter have been a subject of special interest though many decades [1]. This phenomenon manifests itself in systems where quantum instead of thermal fluctuations are relevant. An order-disorder phase transition can occur even at zero temperature, if a suitable parameter (a magnetic field, for example) is tuned externally through the critical region. Simple models, e. g. the pure Ising ferromagnet chain in a transverse field, have been used as prototypes for testing our understanding in the vicinity of such critical points [2]. More interesting still is the criticality found in disordered systems. It has been established that the quantum phase transition in diluted and random Ising models in a transverse field, is controlled by the so-called infinite randomness fixed point (IRFP) [3] which, among other things, is characterized by a divergent dynamical exponent z and an unconventional dynamic scaling [2,4,5].The critical behavior of the quantum disordered and frustrated systems, however, is very poorly understood [1]. Spin glasses are the paradigmatic models of such theoretical challenge and, presumably, their phase transitions should govern by the IRFP [6]. Although recent theoretical works [7][8][9] support this conjecture, old Monte Carlo studies concluded that for two [10] and three [11] dimensions, the quantum phase transition of such systems is instead conventional (with z takes a finite value). Subsequent simulation research has explored this same problem concluding that in two dimensions and at the critical point, several observables (different versions of the Binder cumulant and the correlation length) do not follow a conventional dynamic scaling [12]. Such disagreements are still an open question, which often is circumvented in favor of the IRFP scenario by noting that small system sizes were used in these numerical works. Being that the simulations of disordered and highly frustrated systems as spin glasses inevitably suffer from this drawback, at first sight this obstacle seems impossible to overcome without the use of an alternative strategy.In this paper, we use a quantum parallel-tempering Monte Carlo algorithm to simulate the two-dimensional Ising spin glass model in a transverse magnetic field. Through an exhaustive finite-size scaling analysis of the Binder cumulants, we present new evidence for the existence of an IRFP i...

Geometry of rare regions behind Griffiths singularities in random quantum magnets

“…The SDRG method is expected to provide asymptotically exact results at an infinite disorder fixed point, which has been checked in d = 1 by comparing the results with those of analytical and numerical calculations 12,36 . Also in d = 2 the SDRG results (obtained by the use of the maximum rule) are consistent with quantum Monte Carlo simulations 37,38 . Regarding the Griffiths-phase, the SDRG describes the Griffiths singularities asymptotically exactly in d = 1, where the dynamical exponent is given by the positive root of the equation 35,39,40 (J/h) 1/z av = 1.…”

Geometry of rare regions behind Griffiths singularities in random quantum magnets

“…The SDRG method is expected to provide asymptotically exact results at an infinite disorder fixed point, which has been checked in by comparing the results with those of analytical and numerical calculations 12 , 36 . Also in the SDRG results (obtained by the use of the maximum rule) are consistent with quantum Monte Carlo simulations 37 , 38 . Regarding the Griffiths-phase, the SDRG describes the Griffiths singularities asymptotically exactly in , where the dynamical exponent is given by the positive root of the equation 35 , 39 , 40 .…”

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

“…Since the series for χ SG sees GM singularities rather than critical singularities we can not determine whether or not the QCP is of the infinite-randomness type (for which γ and z are infinite, though γ − 2zν is finite). Recent numerical simulations in two dimensions [26] are argued to support the infinite-randomness scenario, though it seems to us that conventional critical behavior fits the data about as well. As the dimension increases, the effects of GM singularities become much weaker than in d = 2, so we conclude that if the infinite-randomness scenario occurs at all for d > 2, it must manifest itself only over a very small region around the quantum critical point.…”

“…We would like to thank D. A. Matoz-Fernandez for bringing Ref. [26] to our attention. The work of RRPS is supported in part by US NSF grant number DMR-1306048.…”