Diluted antiferromagnets in a field seem to be in a different universality class than the random-field Ising model

We perform large-scale Monte Carlo simulations using the Machta-Newman-Chayes algorithms to study the critical behavior of both the diluted antiferromagnet in a field with 30% dilution and the random-field Ising model with Gaussian random fields for different field strengths. Analytical calculations by Cardy [Phys. Rev. B 29, 505 (1984)] predict that both models map onto each other and share the same universality class in the limit of vanishing fields. However, a detailed finite-size scaling analysis of both the Binder cumulant and the two-point finite-size correlation length suggests that even in the limit of small fields, where the mapping is expected to work, both models are not in the same universality class. Therefore, care should be taken when interpreting (experimental) data for diluted antiferromagnets in a field using the random-field Ising model. Based on our numerical data, we present analytical expressions for the phase boundaries of both models.Comment: 12 pages, 9 figures, 5 table

Interpretation of neutrino flux limits from neutrino telescopes on the Hillas plot

We discuss the interplay between spectral shape and detector response beyond a simple E^-2 neutrino flux at neutrino telescopes, at the example of time-integrated point source searches using IceCube-40 data. We use a self-consistent model for the neutrino production, in which protons interact with synchrotron photons from co-accelerated electrons, and we fully take into account the relevant pion and kaon production modes, the flavor composition at the source, flavor mixing, and magnetic field effects on the secondaries (pions, muon, and kaons). Since some of the model parameters can be related to the Hillas parameters R (size of the acceleration region) and B (magnetic field), we relate the detector response to the Hillas plane. In order to compare the response to different spectral shapes, we use the energy flux density as a measure for the pion production efficiency times luminosity of the source. We demonstrate that IceCube has a very good reach in this quantity for AGN nuclei and jets for all source declinations, while the spectra of sources with strong magnetic fields are found outside the optimal reach. We also demonstrate where neutrinos from kaon decays and muon tracks from tau decays can be relevant for the detector response. Finally, we point out the complementarity between IceCube and other experiments sensitive to high-energy neutrinos, at the example of 2004-2008 Earth-skimming neutrino data from Auger. We illustrate that Auger, in principle, is better sensitive to the parameter region in the Hillas plane from which the highest-energetic cosmic rays may be expected in this model.Comment: 28 pages, 10 figures. Substantial clarifications, such as on definition of "sensitivity" and model descriptio

Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension

The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility and of the correlation length. For dimensions d=6,7 which are larger or equal to the assumed upper critical dimension, d_u=6, mean-field behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.Comment: 8 pages and 13 figures; A consise summary of this work can be found in the papercore database at http://www.papercore.org/Ahrens201

Critical behavior of the Random-Field Ising Magnet with long range correlated disorder

We study the correlated-disorder driven zero-temperature phase transition of the Random-Field Ising Magnet using exact numerical ground-state calculations for cubic lattices. We consider correlations of the quenched disorder decaying proportional to r^a, where r is the distance between two lattice sites and a<0. To obtain exact ground states, we use a well established mapping to the graph-theoretical maximum-flow problem, which allows us to study large system sizes of more than two million spins. We use finite-size scaling analyses for values a={-1,-2,-3,-7} to calculate the critical point and the critical exponents characterizing the behavior of the specific heat, magnetization, susceptibility and of the correlation length close to the critical point. We find basically the same critical behavior as for the RFIM with delta-correlated disorder, except for the finite-size exponent of the susceptibility and for the case a=-1, where the results are also compatible with a phase transition at infinitesimal disorder strength. A summary of this work can be found at the papercore database at www.papercore.org.Comment: 9 pages, 13 figure

Exact dimer ground states for a continuous family of quantum spin chains

Using the matrix product formalism, we define a multi-parameter family of spin models on one dimensional chains, with nearest and next-nearest neighbor anti-ferromagnetic interaction for which exact analytical expressions can be found for its doubly degenerate ground states. The family of Hamiltonians which we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a particular point in this parameter space. Like the Majumdar-Ghosh model, the doubly degenerate ground states of our models have a very simple structure, they are the product of entangled states on adjacent sites. In each of these states there is a non-zero staggered magnetization, which vanishes when we take their translation-invariant combination as the new ground states. At the Majumdar-Ghosh point, these entangled states become the spin-singlets pertaining to this model. We will also calculate in closed form the two point correlation functions, both for finite size of the chain and in the thermodynamic limit.Comment: 11 page

Shock wave compression of iron-silicate garnet

Shock wave Hugoniot data have been obtained for almandine-garnet of composition (Fe_(0.79), Mg_(0.14), Ca_(0.04), Mn_(0.03)) Al_2Si_3O_(12) to pressures of >650 kb. The Hugoniot data indicate the onset of a high-pressure phase at 195 ± 20 kb. Equation-of-state systematics and crystal chemical data (stemming largely from analog compounds) suggest that the high-pressure phase occurs in an ‘ilmenitelike’ structure with an initial density of 4.44 ± 0.04 g/cm^3. This value represents an increase of about 6% over the initial garnet density of 4.180 ± 0.005 g/cm^3. The adiabatic bulk modulus K_0^s and its first pressure derivative (∂K^s/∂P)_T were calculated for the high-pressure phase and found to be 3.19 ± 0.39 Mb and 2.6 ± 0.7, respectively. The major source of probable error in these values results from the indicated uncertainty in the initial density of the high-pressure phase. These results strongly suggest that upper mantle minerals are likely to occur in the ilmenite structure over a substantial part of the lower mantle

Shock induced formation of MgAl_2O_4 spinel from oxides

The physics of mineral grain sliding, which occurs upon dynamic compression of rocks, is investigated by shock loading single crystals of corundum (Al_2O_3) and periclase (MgO) in contact obliquely in impact experiments. Energy dispersive X-ray analysis and X-ray diffraction studies of samples recovered from 26–36 GPa, 800 ns experiments indicated that under certain conditions a spinel phase of composition MgAl_2O_4 and thickness ≤20 µm was produced at the interface between the two crystals. Although the computed shock (continuum) temperatures were below those necessary to melt the initial oxides, the spinel nonetheless appears to have formed as a result of localised melting, via grain boundary sliding friction, followed by rapid quenching. Scanning electron microscopy (SEM) revealed some evidence for such melting. Moreover, the timescale of the experiments is too short for solid state diffusion (during the shock state) to explain the observed spinel thickness, although defect enhanced solid state diffusion, subsequent to loading and unloading, remains a possibility. The results also reinforce other recent observations and theories of heterogeneous deformation in minerals

Shock consolidation of diamond and graphite mixtures to fused polycrystalline diamond

The production of fused compacts of polycrystalline diamond was achieved by subjecting porous (35%–49% porosity) mixtures of diamond crystals plus graphite (13–16 wt. %) to dynamic shock pressures of 10–18 GPa. The recovered material from an initial mixture of 4–8-µm diamond crystals plus graphite revealed a very homogeneous texture with little evidence of original grain boundaries. The preconsolidation addition of graphite also allowed ultrafine (<5 µm) diamond crystals to be consolidated; this was not previously possible with the use of diamond crystals alone. The results are consistent with calculations which suggest that a thin layer of graphite surrounding a diamond crystal delays thermal equilibrium between the surface and interior of the diamond crystal, thus allowing greater surface heating. Consolidation is also probably enhanced by conversion of graphite to diamond, possibly via the liquid state

Moderate velocity oblique impact sliding: Production of shocked meteorite textures and palaeomagnetically important metallic spherules in planetary regoliths

We detail the production of metallic spherules in laboratory oblique shock impact experiments, and their applicability (1) to textures in a partly shock-melted chondritic meteorite and (2) to the occurrence of palaeomagnetically important fine iron or iron alloy particles in the lunar regolith. Samples recovered from 29–44 GPa, 800 ns, experiments revealed melting and textures reminiscent of metallic spherules in the Yanzhuang H-chondrite, including “dumbbell” forms and other more complex morphologies. Our experiments demonstrate that metallic spherules can be produced via oblique impact sliding at lower velocities (1.85 km s^(−1)) than are generally assumed in previous work associated with bulk-shock melting, and that oblique impact sliding is a viable mechanism for producing spherules in shock-induced veins in moderately shocked meteorites. Significantly, our experiments also produced fine metallic (iron alloy) spherules within the theoretical narrow size range (a few tens of nanometers for slightly ellipsoidal particles) for stable single-domain (SSD) particles, which are the most important palaeomagnetically, since they can record lunar and planetary magnetic fields over geological time periods. The experiments also produced spherules consistent with superparamagnetic (SP) and multidomain (MD) particle sizes. The fine SSD and SP particles on the lunar surface are currently thought to have been formed predominantly by space weathering processes. Our experiments suggest that oblique shock impact sliding may be a further means of producing the SSD and SP iron or iron alloy particles observed in the lunar regolith, and which are likely to occur in the regoliths of Mercury and other planetary bodies