Spin glasses on the hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

Geochemistry and lithology of clayey nannofossil ooze turbidites and hemipelagites at ODP Holes 135-834A and 135-835A

The western Lau Basin, between the Central and Eastern Lau Spreading Centers and the Lau Ridge, contains several small, elongate, fault-bounded, partially sediment-filled sub-basins. Sites 834 and 835 were drilled in the oldest part of the Lau Basin in two of these small extensional basins close to the Lau Ridge, formed on late Miocene to early Pliocene oceanic crust. Both sites show a similar sediment sequence that consists of clayey nannofossil oozes and mixed sediments interbedded with epiclastic vitric sands and silts. The vitric sands and silts are largely restricted to the deeper part of the sediment column (early Pliocene-late Pliocene), and the upper part of the sediment column at both sites consists of a distinctive sequence of brown clayey nannofossil ooze, stained by iron and manganese oxyhydroxides (late Pliocene-Holocene). However, the clayey nannofossil ooze sequence at Site 835 is anomalously thick and contains several medium- to very thick beds of matrix-supported, mud-clast conglomerate (interpreted as muddy debris-flow deposits), together with large amounts of redeposited clayey nannofossil ooze and coherent rafted blocks of older hemipelagic material. Redeposited clayey nannofossil oozes can be distinguished from hemipelagic nannofossil oozes using several sedimentological criteria. These include variation in color hue and chroma, presence or absence of bioturbation, presence or absence of scattered foraminifers, grain-size characteristics, variability in calcium carbonate content, presence or absence of pumice clasts, and micropaleontology. Clayey nannofossil ooze turbidites and hemipelagites are also geochemically distinct, with the turbidites being commonly enriched in Mn, Ni, Pb, Zn, Cr, and P. The sediment sequence at Site 835 is dominated by allochthonous sediments, either muddy debris-flow deposits, coherent rafted blocks, or thick clayey nannofossil ooze turbidites. Since 2.9 Ma, only 25% of the 133 m of sediments deposited represents hemipelagic deposition, with an average sedimentation rate of 1.5 cm/k.y.. Allochthonous sediments were the main sediment type deposited during the Brunhes geomagnetic Epoch and make up 80% of the thickness of sediment deposited during this period. Short intervals of mainly hemipelagic deposition occurred from 0.4 to 0.9 Ma, 1.0 to 1.4 Ma, and 1.7 to 2.1 Ma. However, allochthonous sediments were again the dominant sediment type deposited between 2.1 and 2.5 Ma, with a large slide complex emplaced around 2.5 Ma. We conclude that the adjacent high ground, surrounding the basin in which Site 835 was drilled, was affected by marked instability throughout the late Pliocene and Pleistocene. In contrast, sedimentation at Site 834 during this period has been dominated by hemipelagic deposition, with redeposited sediments making up slightly less than 17% of the total thickness of sediment deposited since 2.3 Ma. However, there was a marked increase in frequency and magnitude of redeposited sediments at around 0.2 Ma at Site 834, which broadly corresponds to the onset of a major episode of turbidite and debris-flow emplacement beginning about 0.4 Ma at Site 835. This episode of instability at both sites may be the effect of the approach and passing of the Central Lau propagator at the latitude of Sites 834 and 835 at about 0.5 Ma.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Critical magnetic elds in superconducting systems with semi-metallic bands

In this work, we study the Zeeman splitting effects in the parallel magnetic field versus temperature phase diagram of two-dimensional superconductors with one graphene-like band and the orbital effects of perpendicular magnetic fields in isotropic two-dimensional semi-metallic superconductors. We show that when parallel magnetic fields are applied to graphene and as the intraband interaction decreases to a critical value, the width of the metastability region present in the phase diagram decreases, vanishing completely at that critical value. In the case of two-band superconductors with one graphene-like band, a new critical interaction, associated primarily with the graphene-like band, is required in order for a second metastability region to be present in the phase diagram. For intermediate values of this interaction, a low-temperature first-order transition line bifurcates at an intermediate temperature into a first-order transition between superconducting phases and a second-order transition line between the normal and the superconducting states. In our study on the upper critical fields in generic semi-metallic superconductors, we find that the pair propagator decays faster than that of a superconductor with a metallic band. As result, the zero field band gap equation does not have solution for weak intraband interactions, meaning that there is a critical intraband interaction value in order for a superconducting phase to be present in semi-metallic superconductors. Finally, we show that the out-of-plane critical magnetic field versus temperature phase diagram displays a positive curvature, contrasting with the parabolic-like behaviour typical of metallic superconductors.