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...

We observe the occurrence of an Efros-Shklovskii gap in (Ga,Mn)As based tunnel junctions. The occurrence of the gap is controlled by the extent of the hole wave-function on the Mn acceptor atoms. Using k · p-type calculations we show that this extent depends crucially on the direction of the magnetization in the (Ga,Mn)As (which has two almost equivalent easy axes). This implies one can reversibly tune the system into the insulating or metallic state by changing the magnetization.PACS numbers: 71.30.+h, 75.30.Hx, 75.50.Pp A very direct way to observe the Efros-Shklovskii (ES) gap, the soft gap induced by Coulomb correlations near the Fermi level of a Mott insulator [1,2], is by means of tunnel spectroscopy. Such experiments were, e.g., performed on the (three-dimensional) nonmetallic doped semiconductor Si:B [3, 4] and on thin (two-dimensional) Be films [5]. While both of these experiments employed large area tunnel junctions and a metallic counter electrode, a more recent study employed Ge:As break junctions[6]. This latter approach avoids possible screening of the Coulomb correlations, but the mesoscopic character of the contact may complicate extraction of bulk Coulomb gap behaviour [7].We have recently investigated the physics of a novel type of magnetoresistance, dubbed TAMR (tunneling anisotropic magnetoresistance) [8,9]. TAMR results from the dependence of the density of states (DOS) in strongly spin-orbit coupled ferromagnetic semiconductors, such as (Ga,Mn)As, on the direction of the magnetization of the material. In [9] we reported a drastic (> 10 4 ) increase of the spin-valve signal in a (Ga,Mn)As/GaAs/(Ga,Mn)As tunnel structure on lowering the sample temperature from 4.2 to 1.7 K, and speculated that this behaviour might result from the opening of an ES gap. Here, we provide evidence that the high resistance state of the sample indeed corresponds to a soft-gapped Mott insulator. In these samples, the metalto-insulator transition (MIT) is driven by a large variation of the Bohr radius of a hole bound to a Mn-impurity when the magnetization of the layer is switched from one easy axis to the other. This assignment is supported by a k · p-type calculation of a hydrogen-like impurity in a ferromagnetic GaAs host, extending the successful mean field model for (Ga,Mn)As [11,12].Our (Ga,Mn)As tunnel structure is shown in Fig. 1b. From bottom to top, the Ga 0.94 Mn 0.06 As (100 nm)/ GaAs (2 nm) /Ga 0.94 Mn 0.06 As (10 nm) trilayer stack has been grown by low temperature molecular beam epitaxy (LT-MBE) on a semi-insulating GaAs substrate and a 120 nm undoped GaAs buffer layer. Both (Ga,Mn)As layers are ferromagnetic with an as-grown Curie temperature of ∼ 65 K and highly p-type due to the intrinsic doping arising from the Mn atoms.As seen in the optical micrograph of Fig. 1a, the layer stack is patterned into a square mesa of 100×100 µm 2 by positive optical lithography, metal evaporation, liftoff and wet etching. The top contact is in-situ Ti/Au. Contact to the lower (Ga,Mn)As layer is established by a W/...