Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations

We present results of large-scale Monte Carlo simulations for a three-dimensional Ising model with short range interactions and planar defects, i.e., disorder perfectly correlated in two dimensions. We show that the phase transition in this system is smeared, i.e., there is no single critical temperature, but different parts of the system order at different temperatures. This is caused by effects similar to but stronger than Griffiths phenomena. In an infinite-size sample there is an exponentially small but finite probability to find an arbitrary large region devoid of impurities. Such a rare region can develop true long-range order while the bulk system is still in the disordered phase. We compute the thermodynamic magnetization and its finite-size effects, the local magnetization, and the probability distribution of the ordering temperatures for different samples. Our Monte-Carlo results are in good agreement with a recent theory based on extremal statistics.Comment: 9 pages, 6 eps figures, final version as publishe

Unravelling the controls on the molybdenum isotope ratios of river waters

The molybdenum (Mo) isotope ratios (δ98/95Mo) of river waters control the δ98/95Mo values of seawater and impact on the use of Mo isotope ratios as a proxy of past redox conditions. The δ98/95Mo values of river waters vary by more than 2 ‰, yet the relative roles of lithology versus fractionation during weathering remain contested. Here, we combine measurements from river waters (δ98/95Modiss), river bed materials (δ98/95MoBM) and soils from locations with contrasting lithology. The δ98/95Mo values of river bed materials (δ98/95MoBM), set by rock type, vary by ~1 ‰ between rivers in New Zealand, the Mackenzie Basin, and Iceland. However, the difference between dissolved and solid phase Mo isotopes (Δ98/95Modiss-BM) varies from +0.3 ‰ to +1.0 ‰. We estimate Mo removal from solution using the mobile trace element rhenium and find that it correlates with Δ98/95Modiss-BM across the sample set. The adsorption of Mo to Fe-Mn-(oxyhydr)oxides can explain the observed fractionation. Together, the amount of Mo released through dissolution and taken up by (oxyhydr)oxide formation on land may cause changes in the δ98/95Mo values of rivers, driving long term changes in the Mo isotope ratios of seawater

Unravelling the controls on the molybdenum isotopic composition of rivers

Formation and crystallisation of the Lunar Magma Ocean (LMO) was one of the most incisive events during the early evolution of the Moon. Lunar Magma Ocean solidification concluded with the coeval formation of K-, REE- and P-rich components (KREEP) and an ilmenite-bearing cumulate (IBC) layer. Gravitational overturn of the lunar mantle generated eruptions of basaltic rocks with variable Ti contents, of which their δ49Ti variations may now reflect variable mixtures of ambient lunar mantle and the IBC. To better understand the processes generating the spectrum of lunar low-Ti and high-Ti basalts and the role of Ti-rich phases such as ilmenite, we determined the mass dependent Ti isotope composition of four KREEP-rich samples, 12 low-Ti, and eight high-Ti mare basalts by using a 47Ti-49Ti double spike. Our data reveal significant variations in δ49Ti for KREEP-rich samples (+0.117 to +0.296 ‰) and intra-group variations in the mare basalts (-0.030 to +0.055 ‰ for low-Ti and +0.009 to +0.115 ‰ for high-Ti basalts). We modelled the δ49Ti of KREEP using previously published HFSE data as well as the δ49Ti evolution during fractional crystallisation of the LMO. Both approaches yield δ49TiKREEP similar to measured values and are in excellent agreement with previous studies. The involvement of ilmenite in the petrogenesis of the lunar mare basalts is further evaluated by combining our results with element ratios of HFSE, U and Th, revealing that partial melting in an overturned lunar mantle and fractional crystallisation of ilmenite must be the main processes accounting for mass dependent Ti isotope variations in lunar basalts. Based on our results we can also exclude formation of high-Ti basalts by simple assimilation of ilmenite by ascending melts from the depleted lunar mantle. Rather, our data are in accord with melting of these basalts from a hybrid mantle source formed in the aftermath of gravitational lunar mantle overturn, which is in good agreement with previous Fe isotope data

Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment

In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of quenched randomness, we introduce the idea of rare regions and discuss their importance. We then analyze in detail the different phenomena that can arise at magnetic quantum phase transitions in disordered metals, including quantum Griffiths singularities, smeared phase transitions, and cluster-glass formation. For each scenario, we discuss the resulting phase diagram and summarize the behavior of various observables. We then review several recent experiments that provide examples of these rare region phenomena. We conclude by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative Ising chain fixed, references added, v3: final version as publishe

Ising cubes with enhanced surface couplings

Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor interactions and enhanced couplings between surface spins are studied. In particular, at the surface transition, the corner magnetization shows non-universal, coupling-dependent critical behavior in the thermodynamic limit. Results on the critical exponent of the corner magnetization are compared to previous findings on two-dimensional Ising models with three intersecting defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.

The Ising Susceptibility Scaling Function

We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.Comment: PDFLaTeX, 50 pages, 5 figures, zip file with series coefficients and background data in Maple format provided with the source files. Vs2: Added dedication and made several minor additions and corrections. Vs3: Minor corrections. Vs4: No change to eprint. Added essential square-lattice series input data (used in the calculation) that were removed from University of Melbourne's websit

Felsic crust development in the Kaapvaal Craton, South Africa: A reference sample collection to investigate a billion years of geological history

The crust of the Kaapvaal craton accreted throughout the Archaean over nearly 1 billion years. It provides a unique example of the various geological processes that shape Earth's continental crust, and is illustrated by a reference collection of granitoids and mafic rocks (SWASA collection). This sample collection is fully characterised in term of age, major and trace elements, and documents the following multistage history of the craton. In the Barberton area, the initial stages of accretion (stage B·I, > 3.33 Ga and B.II, 3.28—3.21 Ga) correspond to the formation of a sodic (TTG) crust extracted from a near-chondritic reservoir. Stage B.III (ca. 3.1 Ga) corresponds to reworking of this crust, either through intracrustal melting, or via recycling of some material into the mantle and melting of this enriched mantle. Stage B.IV (2.85—2.7 Ga) corresponds to the emplacement of small, discrete plutons involving limited intracrustal reworking. The Northern Kaapvaal craton corresponds to a mobile belt flanking the Barberton cratonic core to the North. Stage NK·I (> 3.1 Ga) resembles stages B·I and B.II: formation of a TTG crust from a chondritic reservoir. In contrast, stage NK.II. (2.97–2.88 Ga) witnesses probable rifting of a cratonic fragment and formation of greenstone basins as well as a new generation of TTGs with both the mafic and felsic magmatism extracted from an isotopically depleted mantle (super-chondritic) reservoir. Intra-crustal reworking dominates stage NK.III (2.88–2.71 Ga), whereas sanukitoids and related granites, involving a mantle contaminated by recycled crustal material, are common during stage NK.IV (ca. 2.67 Ga)

Global geologic map of asteroid (101955) Bennu indicates heterogeneous resurfacing in the past 500,000 years

Global geologic maps are useful tools for efficient interpretation of a planetary body, and they provide global context for the diversity and evolution of the surface. We used data acquired by the OSIRIS-REx spacecraft to create the first global geologic map of the near-Earth asteroid (101955) Bennu. As this is the first geologic map of a small, non-spherical, rubble-pile asteroid, we discuss the distinctive mapping challenges and best practices that may be useful for future exploration of similar asteroids, such as those to be visited with the Hera and Janus missions. By mapping on two centimeter-scale global image mosaics (2D projected space) and a centimeter-scale global shape model (3D space), we generated three input maps respectively describing Bennu's shape features, geologic features, and surface texture. Based on these input maps, we defined two geologic units: the Smooth Unit and the Rugged Unit. The units are differentiated primarily on the basis of surface texture, concentrations of boulders, and the distributions of lineaments, mass movement features, and craters. They are bounded by several scarps. The Rugged Unit contains abundant boulders and signs of recent mass movement. It also has fewer small (<20 m), putatively fresh craters than the Smooth Unit, suggesting that such craters have been erased in the former. Based on these geologic indicators, we infer that the Rugged Unit has the younger surface of the two. Differential crater size-frequency distributions and the distribution of the freshest craters suggest that both unit surfaces formed ~10–65 million years ago, when Bennu was located in the Main Asteroid Belt, and the Smooth Unit has not been significantly resurfaced in the past 2 million years. Meanwhile, the Rugged Unit has experienced resurfacing within the past ~500,000 years during Bennu's lifetime as a near-Earth asteroid. The geologic units are consistent with global diversity in slope, surface roughness, normal albedo, and thermal emission spectral characteristics. The site on Bennu where the OSIRIS-REx mission collected a regolith sample is located in the Smooth Unit, in a small crater nested within a larger one. So although the Smooth Unit is an older surface than the Rugged Unit, the impact-crater setting indicates that the material sampled was recently exposed. Several similarities are apparent between Bennu and asteroid (162173) Ryugu from a global geologic perspective, including two geologic units distinguishable by variations in the number density of boulders, as well as in other datasets such as brightness