The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte

Network models for localisation problems belonging to the chiral symmetry classes

We consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. We formulate models which have the relevant symmetries and which are generalisations of the network model introduced previously in the context of the integer quantum Hall plateau transition. We show that the generalisations required can be re-expressed as corresponding to the introduction of absorption and amplification into either the original network model, or the variants of it that represent disordered superconductors. In addition, we demonstrate that by imposing appropriate constraints on disorder, a lattice version of the Dirac equation with a random vector potential can be obtained, as well as new types of critical behaviour. These models represent a convenient starting point for analytic discussions and computational studies, and we investigate in detail a two-dimensional example without time-reversal invariance. It exhibits both localised and critical phases, and band-centre singularities in the critical phase approach more closely in small systems the expected asymptotic form than in other known realisations of the symmetry class.Comment: 14 pages, 15 figures, Submitted to Physical Review

Transport via a quantum shuttle

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Isotopic diversity in interplanetary dust particles and preservation of extreme 16O-depletion

Two interplanetary dust particles (IDPs) investigated by NanoSIMS reveal diverse oxygen isotope compositions at the micrometre-scale. The oxygen isotope values recorded at different locations across the single IDP fragments cover a wider range than the bulk values available from all IDPs and bulk meteorites measured to date. Measurement of H, C, and N isotopes by NanoSIMS, and the use of scanning and transmission electron microscopy (SEM and TEM) to determine elemental compositions and textural information allows for a better understanding of the lithologies and organic signatures associated with the oxygen isotope features. IDP Balmoral, a ~15 μm-sized fragment with a chondritic porous (CP)-IDP-like texture, contains a region a few micrometres in size characterised by 16O-depleted isotope signatures in the range δ17O, δ18O = +80‰ to +200‰. The remainder of the fragment has a more 16O-rich composition (δ18O = 0–20‰), similar to many other IDPs and bulk meteorites. Other than in discrete pre-solar grains, such extreme 16O-depletions have only been observed previously in rare components within the matrix of the Acfer 094 meteorite. However, TEM imaging and FeO/MgO/Si ion ratios indicate that the 16O-depleted regions in Balmoral did not form by the same mechanism as that proposed for the 16O-depleted phases in Acfer 094. As the level of 16O depletion is consistent with that expected from isotope selective self-shielding, it is likely that the 16O-depleted reservoir was located close to that where oxygen self-shielding effects were most pronounced (i.e., the outer solar nebula or even interstellar medium). Individual regions within IDP Lumley cover a range in δ18O from −30‰ to +19‰, with the oxygen isotope values broadly co-varying with δD, δ13C, δ15N, light-element ratios and texture. The relationships observed in Lumley indicate that the parent body incorporated material at the micrometre-scale from discrete diverse isotopic reservoirs, some of which are represented by inner Solar System material but others which must have formed in the outer Solar System. The IDP fragments support a model whereby primary dust from the early solar nebula initially formed a variety of reservoirs in the outer solar nebula, with those at lower AU incorporating a higher proportion of inner Solar System chondritic dust than those at larger AU. These reservoirs were subsequently disrupted into micrometre-sized clasts that were re-incorporated into IDP parent bodies, presumably at large AU. These results reveal that any models accounting for mixing processes in the early solar nebula must also account for the presence of an extremely 16O-depleted reservoir in the comet-forming region

The effect of moderate aerobic exercise and relaxation on secretory immunoglobulin A

A deficiency in secretory immunoglobulin A (sIgA) is associated with recurrent upper respiratory tract infections both in the general community and in elite athletes. The aim of this paper was to investigate the effect of aerobic exercise and relaxation on various indices of sIgA in 12 male and 8 female adults who varied in levels of recreational activity. Salivary samples were obtained before, immediately after and 30 minutes after an incremental cycle ergometer test to fatigue, after 30 minutes of cycling at 30 % or 60 % of maximum heart rate, and after 30 minutes of relaxation with guided imagery. Each session was run on a separate day. When expressed in relation to changes in salivary flow rate, sIgA did not change after exercise. However, both the absolute concentration and secretion rate of sIgA increased during relaxation (167 ± 179 μg · ml-1, p < 0.001; and 37 ± 71 μg · min-1, p < 0.05 respectively). Nonspecific protein increased more than sIgA during incremental exercise to fatigue (decrease in the sIgA/protein ratio 92 ± 181 μg · mg protein-1, p < 0.05), but sIgA relative to protein did not change during relaxation. Our findings suggest that sIgA secretion rate is a more appropriate measure of sIgA than sIgA relative to protein, both for exercise and relaxation. These data suggest the possibility of using relaxation to counteract the negative effects of intense exercise on sIgA levels

The effects of stress management on symptoms of upper respiratory tract infection, secretory immunoglobulin A, and mood in young adults

To investigate the efficacy of a stress management programme on symptoms of colds and influenza in 27 university students before and after the examination period. The incidence of symptoms, levels of negative affect, and secretion rate of secretory immunoglobulin A (sIgA) were recorded for 5 weeks before treatment, for the 4 weeks of treatment, and for 8 weeks after treatment in treated subjects and in 25 others who did not participate in stress management. Symptoms decreased in treated subjects but not in controls during and after the examination period. Although sIgA secretion rate increased significantly after individual sessions of relaxation, resting secretion rate of sIgA did not increase over the course of the study. Negative affect decreased after examinations in both groups, but was not affected by treatment. Stress management reduced days of illness independently of negative affect and sIgA secretion rate. Although the component of treatment responsible for this effect has yet to be identified, psychological interventions may have a role in reducing symptoms of upper respiratory tract infection