Thermodynamic Limit for the Ising Model on the Cayley Tree

While the Ising model on the Cayley tree has no spontaneous magnetization at nonzero temperatures in the thermodynamic limit, we show that finite systems of astronomical sizes remain magnetically ordered in a wide temperature range, if the symmetry is broken by fixing an arbitrary single (bulk or surface) spin. We compare the behavior of the finite size magnetization of this model with that of the Ising model on both the Sierpinski Gasket, and the one-dimensional linear chain. This comparison reveals the analogy of the behavior of the present model with the Sierpinski Gasket case.Comment: 5 pages, 4 figure

Critical behavior of 2 and 3 dimensional ferro- and antiferromagnetic spin ice systems in the framework of the Effective Field Renormalization Group technique

In this work we generalize and subsequently apply the Effective Field Renormalization Group technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagome and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin ice model can be exactly mapped to the standard Ising model but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated, and does not order. Antiferromagnetic spin ice (in both 2 and 3 dimensions), is found to undergo a transition to a long range ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced Generalized Constant Coupling method is also applied to the calculation of the critical points and ground state configurations. Again, a very good agreement is found with both exact, Monte Carlo, and renormalization group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.Comment: 28 pages, 9 figures, RevTeX 4 Some minor changes in the conclussions. One reference adde

Tunnelling spectroscopy of the interface between Sr2RuO4 and a single Ru micro-inclusion in eutectic crystals

The understanding of the zero bias conductance peak (ZBCP) in the tunnelling spectra of S/N junctions involving d-wave cuprate superconductors has been important in the determination of the phase structure of the superconducting order parameter. In this context, the involvement of a p-wave superconductor such as Sr2RuO4 in tunnelling studies is indeed of great importance. We have recently succeeded in fabricating devices that enable S/N junctions forming at interfaces between Sr2RuO4 and Ru micro-inclusions in eutectic crystals to be investigated.3 We have observed a ZBCP and have interpreted it as due to the Andreev bound state, commonly seen in unconventional superconductors. Also we have proposed that the onset of the ZBCP may be used to delineate the phase boundary for the onset of a time reversal symmetry broken (TRSB) state within the superconducting state, which does not always coincide with the onset of the superconducting state. However, these measurements always involved two interfaces between Sr2RuO4 and Ru. In the present study, we have extended the previous measurements to obtain a deeper insight into the properties of a single interface between Sr2RuO4 and Ru.Comment: To appear in J. Phys. Soc. Jpn. Vol. 75 No.12 issu

Random Spin-orbit Coupling in Spin Triplet Superconductors: Stacking Faults in Sr_2RuO_4 and CePt_3Si

The random spin-orbit coupling in multicomponent superconductors is investigated focusing on the non-centrosymmetric superconductor CePt_3Si and the spin triplet superconductor Sr_2RuO_4. We find novel manifestations of the random spin-orbit coupling in the multicomponent superconductors with directional disorders, such as stacking faults. The presence of stacking faults is indicated for the disordered phase of CePt_3Si and Sr_2RuO_4. It is shown that the d-vector of spin triplet superconductivity is locked to be d = k_y x - k_x y with the anisotropy \Delta T_c/T_c0 \sim \bar{\alpha}^2/T_c0 W_z, where \bar{\alpha}, T_c0, and W_z are the mean square root of random spin-orbit coupling, the transition temperature in the clean limit, and the kinetic energy along the c-axis, respectively. This anisotropy is much larger (smaller) than that in the clean bulk Sr_2RuO_4 (CePt_3Si). These results indicate that the helical pairing state d = k_y x - k_x y in the eutectic crystal Sr_2RuO_4-Sr_3Ru_2O_7 is stabilized in contrast to the chiral state d = (k_x \pm i k_y) z in the bulk Sr_2RuO_4. The unusual variation of T_c in CePt_3Si is resolved by taking into account the weak pair-breaking effect arising from the uniform and random spin-orbit couplings. These superconductors provide a basis for discussing recent topics on Majorana fermions and non-Abelian statistics.Comment: J. Phys. Soc. Jpn. 79 (2010) 08470

Meaning-making from wordless (or nearly wordless) picturebooks: what educational research expects and what readers have to say

Wordless (or nearly wordless) picturebooks are intriguing in terms of how readers make meaning from them. This article offers a conceptualization of existing studies in the field of education that use wordless picturebooks with young readers. While some of these studies contribute to understanding meaning-making, the pragmatic use of wordless picturebooks often does not take account of their particular nature and of the heightened role of the reader, leading to a mismatch between what the picturebook expects from the implied reader and the researchers’ expectations of what ‘real’ readers must do with these books. By highlighting observations from children’s literature scholarship and reader-response studies, this article aims to encourage a more interdisciplinary understanding of meaning-making. It also seeks to persuade educational researchers and mediators to consider investigative approaches that are not based on verbalization but are more in tune with the invitations that wordless picturebooks extend to young readers

A Triad of Lys12, Lys41, Arg78 Spatial Domain, a Novel Identified Heparin Binding Site on Tat Protein, Facilitates Tat-Driven Cell Adhesion

Tat protein, released by HIV-infected cells, has a battery of important biological effects leading to distinct AIDS-associated pathologies. Cell surface heparan sulfate protoglycans (HSPGs) have been accepted as endogenous Tat receptors, and the Tat basic domain has been identified as the heparin binding site. However, findings that deletion or substitution of the basic domain inhibits but does not completely eliminate Tat–heparin interactions suggest that the basic domain is not the sole Tat heparin binding site. In the current study, an approach integrating computational modeling, mutagenesis, biophysical and cell-based assays was used to elucidate a novel, high affinity heparin-binding site: a Lys12, Lys41, Arg78 (KKR) spatial domain. This domain was also found to facilitate Tat-driven β1 integrin activation, producing subsequent SLK cell adhesion in an HSPG-dependent manner, but was not involved in Tat internalization. The identification of this new heparin binding site may foster further insight into the nature of Tat-heparin interactions and subsequent biological functions, facilitating the rational design of new therapeutics against Tat-mediated pathological events

Evaluation of Spin-Triplet Superconductivity in Sr2RuO4

This review presents a summary and evaluations of the superconducting properties of the layered ruthenate Sr2RuO4 as they are known in the autumn of 2011. This paper appends the main progress that has been made since the preceding review by Mackenzie and Maeno was published in 2003. Here, special focus is placed on the critical evaluation of the spin-triplet, odd-parity pairing scenario applied to Sr2RuO4. After an introduction to superconductors with possible odd-parity pairing, accumulated evidence for the pairing symmetry of Sr2RuO4 is examined. Then, significant recent progress on the theoretical approaches to the superconducting pairing by Coulomb repulsion is reviewed. A section is devoted to some experimental properties of Sr2RuO4 that seem to defy simple explanations in terms of currently available spin-triplet scenario. The next section deals with some new developments using eutectic boundaries and micro-crystals, which reveals novel superconducting phenomena related to chiral edge states, odd-frequency pairing states, and half-fluxoid states. Some of these properties are intimately connected with the properties as a topological superconductor. The article concludes with a summary of knowledge emerged from the study of Sr2RuO4 that are now more widely applied to understand the physics of other unconventional superconductors, as well as with a brief discussion of relatively unexplored but promising areas of ongoing and future studies of Sr2RuO4.Comment: 31 pages, 35 figures, published in J. Phys. Soc. Jpn. as a review article of Special Topic

Increasing the Astrophysical Reach of the Advanced Virgo Detector via the Application of Squeezed Vacuum States of Light

Current interferometric gravitational-wave detectors are limited by quantum noise over a wide range of their measurement bandwidth. One method to overcome the quantum limit is the injection of squeezed vacuum states of light into the interferometer’s dark port. Here, we report on the successful application of this quantum technology to improve the shot noise limited sensitivity of the Advanced Virgo gravitational-wave detector. A sensitivity enhancement of up to 3.2±0.1  dB beyond the shot noise limit is achieved. This nonclassical improvement corresponds to a 5%–8% increase of the binary neutron star horizon. The squeezing injection was fully automated and over the first 5 months of the third joint LIGO-Virgo observation run O3 squeezing was applied for more than 99% of the science time. During this period several gravitational-wave candidates have been recorded

Quantum Backaction on kg-Scale Mirrors: Observation of Radiation Pressure Noise in the Advanced Virgo Detector

The quantum radiation pressure and the quantum shot noise in laser-interferometric gravitational wave detectors constitute a macroscopic manifestation of the Heisenberg inequality. If quantum shot noise can be easily observed, the observation of quantum radiation pressure noise has been elusive, so far, due to the technical noise competing with quantum effects. Here, we discuss the evidence of quantum radiation pressure noise in the Advanced Virgo gravitational wave detector. In our experiment, we inject squeezed vacuum states of light into the interferometer in order to manipulate the quantum backaction on the 42 kg mirrors and observe the corresponding quantum noise driven displacement at frequencies between 30 and 70 Hz. The experimental data, obtained in various interferometer configurations, is tested against the Advanced Virgo detector quantum noise model which confirmed the measured magnitude of quantum radiation pressure noise