We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains reference to related work in cond-mat/950412

Numerical results up to 42nd order of replica symmetry breaking (RSB) are used to predict the singular structure of the SK spin glass at T = 0. We confirm predominant single parameter scaling and derive corrections for the T = 0 order function q(a), related to a Langevin equation with pseudotime 1/a. a = 0 and a = ∞ are shown to be two critical points for ∞-RSB, associated with two discrete spectra of Parisi block size ratios, attached to a continuous spectrum. Finite-RSB-sizescaling, associated exponents, and T = 0-energy are obtained with unprecedented accuracy.PACS numbers: 75.10. Hk,75.10.Nr,75.40.Cx The low temperature limit usually simplifies considerably the properties of magnetically ordered phases. Research in recent decades has however shown that frustrated systems can have rich behaviour even at T = 0. Spin glasses [1] are an extreme example from condensed matter, while others are a feature of computer and information science in problems such as hard satisfiability and error-correcting codes. In particular, even the potentially soluble infinite-range Ising spin glass model of Sherrington and Kirkpatrick [2] has left open many puzzling questions. Parisi devised an ansatz [3] for the order parameter of the SK-model, based on an infinite hierarchy of so-called replica symmetry breakings and related hierarchically to the distribution of overlaps of metastable solutions [10]. The determining equations for this ansatz have recently been rigorously proven to be exact [4], but its explicit solution remains elusive. Also only recently has the T = 0 SK problem been recognized as a critical one-dimensional theory [5,6].In view of the paradigmic role that the SK-model has played in the understanding and development of the statistical physics of complex systems, together with the potential that further comprehension of its subtleties has for extensions to other more-complicated systems in many fields of science, especially those involving zero-(or effectively zero-)temperature replica-symmetry-breaking [17] transitions, it seems important to pursue the better understanding of T = 0 RSB in the SK model. This letter is concerned with such a study and the exposure of several novel features, including new critical spectra, invariance points and quasi-dynamics.Parisi's order parameter is a function q(x, T ) on an interval 0 ≤ x ≤ 1, the limit of a stepwise function q i (T ), x i (T ) determined by extremization of a free energy. It provides the hierarchical distribution of pure state overlaps P (q) through P (q) = dx/dq [10]. Parisi's original work considered numerically an approximation with a small finite number of steps, but most recent studies of the SK model have been based on self-consistent solutions for his later non-trivial continuous order function, typically perturbatively in the deviation from the finite-temperature phase transition. Here the analysis is considered explicitly at T = 0 using very accurate studies of a very large sequence of RSB orders.In the limit of zero temperature Parisi's order functi...

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Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0 a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.