Lattice model theory of the equation of state covering the gas, liquid, and solid phases

The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon

Evidence for Isospin Violation and Measurement of C P Asymmetries in B → K ∗ ( 892 ) γ

We report the first evidence for isospin violation in B→K∗γ and the first measurement of the difference of CP asymmetries between B+→K*+γ and B0→K*0γ. This analysis is based on the data sample containing 772×106B¯B pairs that was collected with the Belle detector at the KEKB energy-asymmetric e+e− collider. We find evidence for the isospin violation with a significance of 3.1σ, Δ0+=[+6.2±1.5(stat)±0.6(syst)±1.2(f+−/f00)]%, where the third uncertainty is due to the uncertainty on the fraction of B+B− to B0¯B0 production in Υ(4S) decays. The measured value is consistent with predictions of the standard model. The result for the difference of CP asymmetries is ΔACP=[+2.4±2.8(stat)±0.5(syst)]%, consistent with zero. The measured branching fractions and CP asymmetries for charged and neutral B meson decays are the most precise to date. We also calculate the ratio of branching fractions of B0→K*0γ to B0s→ϕγ

A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0

We present a formalism for computing the complexity of metastable states and the zero-temperature magnetic hysteresis loop in the soft-spin random-field model in finite dimensions. The complexity is obtained as the Legendre transform of the free-energy associated to a certain action in replica space and the hysteresis loop above the critical disorder is defined as the curve in the field-magnetization plane where the complexity vanishes; the nonequilibrium magnetization is therefore obtained without having to follow the dynamical evolution. We use approximations borrowed from condensed-matter theory and based on assumptions on the structure of the direct correlation functions (or proper vertices), such as a local approximation for the self-energies, to calculate the hysteresis loop in three dimensions, the correlation functions along the loop, and the second moment of the avalanche-size distribution.Comment: 28 pages, 12 figure

Monte Carlo Study of the Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice

We report a Monte Carlo study of the classical antiferromagnetic Heisenberg model with easy axis anisotropy on the triangular lattice. Both the free energy cost for long wavelength spin waves as well as for the formation of free vortices are obtained from the spin stiffness and vorticity modulus respectively. Evidence for two distinct Kosterlitz-Thouless types of defect-mediated phase transitions at finite temperatures is presented.Comment: 8 pages, 10 figure

Ultrasound Biomicroscopy Comparison of Ab Interno

Purpose. To compare ab interno and ab externo scleral fixation of posterior chamber intraocular lenses (PCIOL) using ultrasound biomicroscopy (UBM). Methods. Randomized patients underwent ab externo or ab interno scleral fixation of a PCIOL. Ultrasound biomicroscopy was performed 3 to 6 months postoperatively, to determine PCIOL centration, IOL distance to the iris at 12, 3, 6, and 9 hours, and haptics placement in relation to the ciliary sulcus. Results. Fifteen patients were enrolled in the study. The ab externo technique was used in 7 eyes (46.6%) and the ab interno in 8 eyes (53.3%). In the ab externo technique, 14 haptics were located: 4 (28.57%) in the ciliary sulcus; 2 (14.28%) anterior to the sulcus; and 8 (57.14%) posterior to the sulcus, 6 in the ciliary body and 2 posterior to the ciliary body. In the ab interno group, 4 haptics (25.0%) were in the ciliary sulcus, 2 (12.50%) anterior to the sulcus, and 10 (75.0%) posterior to the sulcus, 4 in the ciliary body and 6 posterior to the ciliary body. Conclusions. Ab externo and ab interno scleral fixation techniques presented similar results in haptic placement. Ab externo technique presented higher vertical tilt when compared to the ab interno

Zero-Temperature Phase Transitions of Antiferromagnetic Ising Model of General Spin on a Triangular Lattice

We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a triangular lattice to an interface model whose entropic fluctuations are proposed to be described by an effective Gaussian free energy, which enables us to calculate the critical exponents of various operators in terms of the stiffness constant of the interface. Monte Carlo simulations for the ground-state ensemble utilizing this interfacial representation are performed to study both the dynamical and the static properties of the model. This method yields more accurate numerical results for the critical exponents. By varying the spin magnitude in the model, we find that the model exhibits three phases with a Kosterlitz-Thouless phase transition at 3/2<S_{KT}<2 and a locking phase transition at 5/2 < S_L \leq 3. The phase diagram at finite temperatures is also discussed.Comment: 15 pages, LaTeX; 10 figures in PostScript files; The revised version appears in PRB (see Journal-ref). New electronic address of first author, [email protected]

Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.90.+m, 02.70.-cComment: RevTeX style, 20 pages, 12 figure

Thermal phase diagrams of columnar liquid crystals

In order to understand the possible sequence of transitions from the disordered columnar phase to the helical phase in hexa(hexylthio)triphenylene (HHTT), we study a three-dimensional planar model with octupolar interactions inscribed on a triangular lattice of columns. We obtain thermal phase diagrams using a mean-field approximation and Monte Carlo simulations. These two approaches give similar results, namely, in the quasi one-dimensional regime, as the temperature is lowered, the columns order with a linear polarization, whereas helical phases develop at lower temperatures. The helicity patterns of the helical phases are determined by the exact nature of the frustration in the system, itself related to the octupolar nature of the molecules.Comment: 12 pages, 9 figures, ReVTe

Strong Coupling Quantum Gravity and Physics beyond the Planck Scale

We propose a renormalization prescription for the Wheeler-DeWitt equation of (3+1)-dimensional Einstein gravity and also propose a strong coupling expansion as an approximation scheme to probe quantum geometry at length scales much smaller than the Planck length. We solve the Wheeler-DeWitt equation to the second order in the expansion in a class of local solutions and discuss problems arising in our approach.Comment: 27 pages, LaTeX file. To be published in Phys. Rev.