Surface tension in the dilute Ising model. The Wulff construction

We study the surface tension and the phenomenon of phase coexistence for the Ising model on \mathbbm{Z}^d ($d \geqslant 2$) with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random couplings) of surface tension and analyze its large deviations : upper deviations occur at volume order while lower deviations occur at surface order. We study the asymptotics of surface tension at low temperatures and relate the quenched value $\tau^q$ of surface tension to maximal flows (first passage times if $d = 2$). For a broad class of distributions of the couplings we show that the inequality $\tau^a \leqslant \tau^q$ -- where $\tau^a$ is the surface tension under the averaged Gibbs measure -- is strict at low temperatures. We also describe the phenomenon of phase coexistence in the dilute Ising model and discuss some of the consequences of the media randomness. All of our results hold as well for the dilute Potts and random cluster models

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^\zeta$, is consistent with the theoretical prediction $\zeta = 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $\theta$, which determines the violation of hyperscaling, the correlation length exponent $\nu$, and the magnetization exponent $\beta$. The value $\beta = 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure

Geometric effects on T-breaking in p+ip and d+id superconductors

Superconducting order parameters that change phase around the Fermi surface modify Josephson tunneling behavior, as in the phase-sensitive measurements that confirmed $d$ order in the cuprates. This paper studies Josephson coupling when the individual grains break time-reversal symmetry; the specific cases considered are $p \pm ip$ and $d \pm id$, which may appear in Sr$_2$RuO$_4$ and Na$_x$CoO$_2 \cdot$(H$_2$O)$_y$ respectively. $T$-breaking order parameters lead to frustrating phases when not all grains have the same sign of time-reversal symmetry breaking, and the effects of these frustrating phases depend sensitively on geometry for 2D arrays of coupled grains. These systems can show perfect superconducting order with or without macroscopic $T$-breaking. The honeycomb lattice of superconducting grains has a superconducting phase with no spontaneous breaking of $T$ but instead power-law correlations. The superconducting transition in this case is driven by binding of fractional vortices, and the zero-temperature criticality realizes a generalization of Baxter's three-color model.Comment: 8 page

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

Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review article. This version corrects two further typographic errors (three total with respect to the published version), see page 2 for detail

Defects and glassy dynamics in solid He-4: Perspectives and current status

We review the anomalous behavior of solid He-4 at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in He-4. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid He-4. Our proposed glass model for solid He-4 has several implications: (1) The anomalous properties of He-4 can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid He-4 is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich He-4 crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in He-4.Comment: 33 pages, 13 figure

Involvement of miRNAs in the differentiation of human glioblastoma multiforme stem-like cells

Glioblastoma multiforme (GBM)-initiating cells (GICs) represent a tumor subpopulation with neural stem cell-like properties that is responsible for the development, progression and therapeutic resistance of human GBM. We have recently shown that blockade of NFκB pathway promotes terminal differentiation and senescence of GICs both in vitro and in vivo, indicating that induction of differentiation may be a potential therapeutic strategy for GBM. MicroRNAs have been implicated in the pathogenesis of GBM, but a high-throughput analysis of their role in GIC differentiation has not been reported. We have established human GIC cell lines that can be efficiently differentiated into cells expressing astrocytic and neuronal lineage markers. Using this in vitro system, a microarray-based high-throughput analysis to determine global expression changes of microRNAs during differentiation of GICs was performed. A number of changes in the levels of microRNAs were detected in differentiating GICs, including over-expression of hsa-miR-21, hsa-miR-29a, hsa-miR-29b, hsa-miR-221 and hsa-miR-222, and down-regulation of hsa-miR-93 and hsa-miR-106a. Functional studies showed that miR-21 over-expression in GICs induced comparable cell differentiation features and targeted SPRY1 mRNA, which encodes for a negative regulator of neural stem-cell differentiation. In addition, miR-221 and miR-222 inhibition in differentiated cells restored the expression of stem cell markers while reducing differentiation markers. Finally, miR-29a and miR-29b targeted MCL1 mRNA in GICs and increased apoptosis. Our study uncovers the microRNA dynamic expression changes occurring during differentiation of GICs, and identifies miR-21 and miR-221/222 as key regulators of this process

Standing stock of Antarctic krill (Euphausia superba Dana, 1850) (Euphausiacea) in the Southwest Atlantic sector of the Southern Ocean, 2018–19

Estimates of the distribution and density of Antarctic krill (Euphausia superba Dana, 1850) were derived from a large-scale survey conducted during the austral summer in the Southwest Atlantic sector of the Southern Ocean and across the Scotia Sea in 2018–19, the ‘2018–19 Area 48 Survey’. Survey vessels were provided by Norway, the Association of Responsible Krill harvesting companies and Aker BioMarine AS, the United Kingdom, Ukraine, Republic of Korea, and China. Survey design followed the transects of the Commission for the Conservation of Antarctic Marine Living Resources synoptic survey, carried out in 2000 and from regular national surveys performed in the South Atlantic sector by the U.S., China, Republic of Korea, Norway, and the U.K. The 2018–19 Area 48 Survey represents only the second large-scale survey performed in the area and this joint effort resulted in the largest ever total transect line (19,500 km) coverage carried out as one single exercise in the Southern Ocean. We delineated and integrated acoustic backscatter arising from krill swarms to produce distribution maps of krill areal biomass density and standing stock (biomass) estimates. Krill standing stock for the Area 48 was estimated to be 62.6 megatonnes (mean density of 30 g m–2 over 2 million km2) with a sampling coefficient variation of 13%. The highest mean krill densities were found in the South Orkney Islands stratum (93.2 g m–2) and the lowest in the South Georgia Island stratum (6.4 g m–2). The krill densities across the strata compared to those found during the previous survey indicate some regional differences in distribution and biomass. It is currently not possible to assign any such differences or lack of differences between the two survey datasets to longer term trends in the environment, krill stocks or fishing pressure

The tumor microenvironment underlies acquired resistance to CSF-1R inhibition in gliomas.

Macrophages accumulate with glioblastoma multiforme (GBM) progression and can be targeted via inhibition of colony-stimulating factor-1 receptor (CSF-1R) to regress high-grade tumors in animal models of this cancer. However, whether and how resistance emerges in response to sustained CSF-1R blockade is unknown. We show that although overall survival is significantly prolonged, tumors recur in >50% of mice. Gliomas reestablish sensitivity to CSF-1R inhibition upon transplantation, indicating that resistance is tumor microenvironment-driven. Phosphatidylinositol 3-kinase (PI3K) pathway activity was elevated in recurrent GBM, driven by macrophage-derived insulin-like growth factor-1 (IGF-1) and tumor cell IGF-1 receptor (IGF-1R). Combining IGF-1R or PI3K blockade with CSF-1R inhibition in recurrent tumors significantly prolonged overall survival. Our findings thus reveal a potential therapeutic approach for treating resistance to CSF-1R inhibitors