Geometric effects on critical behaviours of the Ising model

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties the Ising model when the lattice is embedded on negatively curved surfaces.Comment: 16 pages, 6 figures, to appear in J. Phys. A: Math. Ge

Measurement of the 2H(n,γ)3H reaction cross section between 10 and 550 keV

We have measured for the first time the cross section of the 2H(n,γ)3H reaction at an energy relevant to big-bang nucleosynthesis by employing a prompt discrete -ray detection method. The outgoing photons have been detected by means of anti-Compton NaI(Tl) spectrometers with a large signal-to-noise ratio. The resulting cross sections are 2.23±0.34,1.99±0.25, and 3.76±0.41µb at En=30.5,54.2, and 531 keV, respectively. At En=30.5 keV the cross section differs from the value reported previously by a factor of 2. Based on the present data the reaction rate has been obtained for temperatures in the range 107-1010 K. The astrophysical impact of the present result is discussed. The obtained cross sections are compared with a theoretical calculation based on the Faddeev approach, which includes meson exchange currents as well as a three-nucleon force

Phonon dispersion and electron-phonon interaction in peanut-shaped fullerene polymers

We reveal that the periodic radius modulation peculiar to one-dimensional (1D) peanut-shaped fullerene (C$_{60}$) polymers exerts a strong influence on their low-frequency phonon states and their interactions with mobile electrons. The continuum approximation is employed to show the zone-folding of phonon dispersion curves, which leads to fast relaxation of a radial breathing mode in the 1D C$_{60}$ polymers. We also formulate the electron-phonon interaction along the deformation potential theory, demonstrating that only a few set of electron and phonon modes yields a significant magnitude of the interaction relevant to the low-temperature physics of the system. The latter finding gives an important implication for the possible Peierls instability of the C$_{60}$ polymers suggested in the earlier experiment.Comment: 9 pages, 8 figure

Periodic boundary conditions on the pseudosphere

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems and we illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.Comment: 30 pages, minor corrections, accepted to J. Phys.

Theory of Room Temperature Ferromagnet V(TCNE)_x (1.5 < x < 2): Role of Hidden Flat Bands

Theoretical studies on the possible origin of room temperature ferromagnetism (ferromagnetic once crystallized) in the molecular transition metal complex, V(TCNE)_x (1.5<x<2) have been carried out. For this family, there have been no definite understanding of crystal structure so far because of sample quality, though the effective valence of V is known to be close to +2. Proposing a new crystal structure for the stoichiometric case of x=2, where the valence of each TCNE molecule is -1 and resistivity shows insulating behavior, exchange interaction among d-electrons on adjacent V atoms has been estimated based on the cluster with 3 vanadium atoms and one TCNE molecule. It turns out that Hund's coupling among d orbitals within the same V atoms and antiferromagnetic coupling between d oribitals and LUMO of TCNE (bridging V atoms) due to hybridization result in overall ferromagnetism (to be precise, ferrimagnetism). This view based on localized electrons is supplemented by the band picture, which indicates the existence of a flat band expected to lead to ferromagnetism as well consistent with the localized view. The off-stoichiometric cases (x<2), which still show ferromagnetism but semiconducting transport properties, have been analyzed as due to Anderson localization.Comment: Accepted for publication in J. Phys. Soc. Jpn. Vol.79 (2010), No. 3 (March issue), in press; 6 pages, 8 figure

On the Accuracy of Hyperspherical Harmonics Approaches to Photonuclear Reactions

Using the Lorentz Integral Transform (LIT) method we compare the results for the triton total photodisintegration cross section obtained using the Correlated Hyperspherical Harmonics (CHH) and the Effective Interaction Hyperspherical Harmonics (EIHH) techniques. We show that these two approaches, while rather different both conceptually and computationally, lead to results which coincide within high accuracy. The calculations which include two- and three-body forces are of the same high quality in both cases. We also discuss the comparison of the two approaches in terms of computational efficiency. These results are of major importance in view of applications to the much debated case of the four-nucleon photoabsorption.Comment: 12 pages, 3 figure