Finite-Size Effects for the Potts Model with Weak Boundary Conditions

Using the Pirogov–Sinai theory, we study finite-size effects for the ferromagnetic q-state Potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions. If the surface coupling is about half of the bulk coupling and q is sufficiently large, we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume. This allows a rigorous control of the finite-size effects for these weak boundary conditions. In particular, we give explicit formulæ for the rounding of the infinite-volume jumps of the internal energy and magnetization, as well as the position of the maximum of the finite-volume specific heat. While the width of the rounding window is of order L ^–d , the same as for periodic boundary conditions, the shift is much larger, of order L ^–1. For strong boundary conditions—the surface coupling is either close to zero or close to the bulk coupling—the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase, respectively. In particular, it means that sufficiently small boundary fields lead to the disordered, and not to the ordered Gibbs state. This gives an explicit proof of A. van Enter's result that the phase transition in the Potts model is not robust.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

An On-Line Library of Extended High-Temperature Expansions of Basic Observables for the Spin-S Ising Models on Two- and Three-Dimensional Lattices

We present an on-line library of unprecedented extension for high-temperature expansions of basic observables in the Ising models of general spin S, with nearest-neighbor interactions. We have tabulated through order ²⁵ the series for the nearest-neighbor correlation function, the susceptibility and the second correlation moment in two dimensions on the square lattice, and, in three dimensions, on the simple-cubic and the body-centered cubic lattices. The expansion of the second field derivative of the susceptibility is also tabulated through ²³ for the same lattices. We have thus added several terms (from four up to thirteen) to the series already published for spin S = 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 5, .     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

Gamma-ray spectroscopy of the neutron-rich Ni region through heavy-ion deep-inelastic collisions

Nuclei in the neutron-rich Ni region have been studied by γ-ray spectroscopy. Gamma-rays emitted from isomers, with T _1/2 > 1 ns, produced in heavy-ion deep-inelastic collisions were measured with an isomer-scope. The nuclear structure of the doubly magic ⁶⁸Ni and its neighbor ^69,71Cu is discussed on the basis of the shell model. Future experiments for more neutron-rich Ni nuclei are also viewed. Received: 1 May 2001 / Accepted: 4 December 2001     

Scale Invariance of the PNG Droplet and the Airy Process

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single time (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y ^–2. Roughly the Airy process describes the last line of Dyson's Brownian motion model for random matrices. Our construction uses a multi-layer version of the PNG model, which can be analyzed through fermionic techniques. Specializing our result to a fixed value of y, one reobtains the celebrated result of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation.     

Simulation of a High Harmonic Gyrotron with Axis-Encircling Electron Beam and Permanent Magnet

A computer code for simulation of beam-field interaction in a resonant cavity of a gyrotron has been developed. It is based on a self-consistent, time-independent, single-mode physical model. The code has been applied to the analysis of the electrodynamical system of a novel high-harmonic gyrotron with axis-encircling beam and a permanent magnet. In this paper both the physical model and numerical techniques used are outlined. Some results of the numerical experiments are presented and discussed.     

Shell model interaction between proton holes and between proton holes and neutron particles around 208Pb

An effective residual interaction between particles and holes for shell model calculations around ²⁰⁸Pb, derived from the interaction between free nucleons, is compared with the measured properties of proton-hole neutron states in ²⁰⁸Tl and the interaction between proton holes is adjusted to newly measured level energies in ²⁰⁶Hg. These interaction elements are particularly relevant for neutron-rich nuclei. The adjustment of two mixing elements reproduces the known γ-decay data in ²⁰⁸Tl. Received: 2 April 2002 / Accepted: 2 May 2002     

高里德伯态氢原子与氢分子的全量子态分辨的散射动力学研究:费米模型的精确性

文章描述了高里德伯态氢原子与氘分子（D2）散射的近期研究结果。实验研究表明，在高里德伯态氢原子与D2的散射中，非弹性散射和化学反应散射都是重要的。在非弹性散射过程中，氘分子的核自旋是守恒的。反应散射结果说明，高里德伯态氢原子与氘分子的散射动力学和质子与氘分子的散射动力学是非常类似的．这一结果表明，费米的独立碰撞模型在态-态散射动力学的层次上也是正确的。