Possible extinction of Berezinskii–Kosterlitz–Thouless transition by diagonal interactions in the checkerboard lattice

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of a diagonal crossing (coupling constant $J^{\prime }$) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the $O(3)$ symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an $O(2)$ symmetry, a Berezinskii–Kosterlitz–Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants $J^{\prime }$ and D. The problem is developed through a continuous representation given by the $O(3)$ Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model.     

Berezinskii–Kosterlitz–Thouless transition in two-dimensional arrays of Josephson coupled Bose–Einstein condensates

We study the phase transition occurring in Bose–Einstein condensates placed in an optical lattice where the system is arranged in a form of a two-dimensional bosonic Josephson junction array. It is shown that the Josephson interaction between adjacent condensates (trapped in the valleys of the periodic lattice potential) can trigger Berezinskii–Kosterlitz–Thouless transition at a finite temperature _TKT$T_{\mathit{KT}}$ to the ordered state composed of bound vortex–antivortex phase-field configurations of individual condensates. Using a lattice model of the bosonic Josephson junction array, we derive the effective phase-only Hamiltonian and calculate the critical temperature _TKT$T_{\mathit{KT}}$. Finally, we discuss the results in the context of system parameters and possible experiments.     

First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau’s two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii–Kosterlitz–Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. These predictions might be readily examined in current experimental setups for 2D dilute Bose gases with a sufficiently large number of atoms, where the finite-size effect due to harmonic traps is relatively weak.     

A scheme to observe universal breathing mode and Berezinskii–Kosterlitz–Thouless phase transition in a two-dimensional photon gas

A system of two-dimensional photon gas has recently been realized experimentally. We show that this setup can be used to observe a universal breathing mode of photon gas and a modification in the experimental setup would open up a possibility of observing the Berezinskii–Kosterlitz–Thouless (BKT) phase transition in such a system. Furthermore, the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.     

Kosterlitz–Thouless transition,spectral property and magnetic moment for a two-dot structure with level difference

By means of the numerical renormalization group method, we study the phase transition, the spectral property, and the temperature-dependent magnetic moment for a parallel double dot system with level difference, where the dot energies are kept symmetric to the half-filled level. A Kosterlitz–Thouless(KT) transition between local spin triplet and singlet is found. In the triplet regime, the local spin is partially screened by the conduction leads and spin-1 Kondo effect is realized.While for the singlet, the Kondo peak is strongly suppressed and the magnetic moment decreases to 0 at a definite low temperature. We attribute this KT transition to the breaking of the reflection symmetry, resulting from the difference of the charge occupations of the two dots. To understand this KT transition and related critical phenomena, detailed scenarios are given in the transmission coefficient and the magnetic moment, and an effective Kondo model refers to the RayleighSchrdinger perturbation theory is used.     

Voltage-controlled Kosterlitz–Thouless transitions and various kinds of Kondo behaviors in a triple dot device

The transport property and phase transition for a parallel triple dot device are studied by adopting Wilson's numerical renormalization group technique, focusing on the effects of level spacings between neighboring dot sites. By keeping dot 2at the half-filled level and tuning the level differences, it is demonstrated that the system transits from local spin quadruplet to triplet and doublet sequently, and three kinds of Kondo peaks at the Fermi surface could be found, which are separated by two Kosterlitz–Thouless type quantum phase transitions and correspond to spin-3/2, spin-1, and spin-1/2 Kondo effect,respectively. To obtain a detailed understanding of these problems, the charge occupation, the spin–spin correlation, the transmission coefficient, and the temperature-dependent magnetic moment are shown, and necessary physical arguments are given.     

Isoscalar amplitude dominance in e + e − annihilation to N N̄ pair close to the threshold

We use the Paris nucleon-antinucleon optical potential for explanation of experimental data in the process e ⁺ e ^? → p p? near threshold. It turns out that final-state interaction due to Paris optical potential allows us to reproduce available experimental data. It follows from our consideration that the isoscalar form factor is much larger than the isovector one.     

Directed polymer – directed percolation transition: the strong disorder case

The transition of physical properties in disordered systems from strong disorder characteristics to weak disorder characteristics is studied for the directed polymer case. It is shown analytically that this transition is governed by the ratio (pc)/k, where is the probability density of the maximal bond of the optimal Min-Max path, pc is the critical probability of directed percolation, and k is the degree of disorder. This analytic result is found to be in agreement with numerical results related to this transition.     

On production of η′ mesons in pp collisions close to threshold

The near threshold behaviour of the reaction cross section for pp→ppη^′, recently measured in experiments at COSY and SATURNE, is analyzed. The interaction in the pp as well as in the η^′ p final states is taken into account. The suppression of the total cross section for this process at excess energies Q < 3 MeV observed in these experiments is interpreted as an evidence for a strong repulsive η^′ p interaction. Received: 26 May 1999 / Revised version: 8 July 1999     

Photoproduction of η and η' mesons off nucleons close to threshold

The importance of Born terms and resonance exchange for η and η' photoproduction off both the proton and neutron within U(3) baryon chiral perturbation theory is investigated. Low-lying resonances such as the vector mesons and J ^P = 1/2⁺, 1/2^- baryon resonances are included explicitly and their contributions together with the Born terms are calculated. The coupling constants of the resonances are determined from strong and radiative decays. We obtain reasonable agreement with experimental data near threshold. Received: 17 March 2000 / Accepted: 8 September 2000     

Temperature dependence of Bi2O3 structural parameters close to the α–δ phase transition

This article presents the results of in situ X-ray powder diffraction, Raman spectroscopy, and electrical impedance spectroscopy of the α-phase of Bi₂O₃, at 0.1 MPa in the temperature range below and above the α–δ-phase transition. This work demonstrated subtle nonlinear temperature variations of the cell parameters, of the hard-mode Raman shift, and of the activation energy of electrical conductivity in the temperature range about 100–120°C below the α–δ phase transition temperature T _Tr ≈ 725°C in Bi₂O₃. At T < 600°C, the linear variation of the inverse dielectric susceptibility (χ ^?1) correlates well with the hard mode frequency shift Δ(ω ²) of Raman A_1g mode as Δ(χ ^?1)/Δ(ω ²) ≈ 5.5 × 10^?7 cm². A structural model describing the mechanism of O^2? anion distribution and electric dipole disordering in the vicinity of T _Tr is discussed.     

Can the glass transition in bulk polymers be modeled by percolation picture?

Recent observations (Eur. Phys. J. E 9, 135 (2002)) showed that the vitrification process, which sets in during the linear bulk methyl methacrylate (MMA) polymerization carried out below glass transition temperatures, can be modelled by static percolation picture. To generalize this observation for different kind of bulk linear or crosslinked polymers not enough data are present in the literature. To cover partly this deficit we studied the glass transition of MMA and styrene (Sty) crosslinking copolymerization in varying ratios of MMA and Sty. Both the fluorescence intensity I and the lifetime of pyrene (Py) used as a nanosecond in situ fluoroprobe were monitored during the gelation time. Both I and increase dramatically as a result of the reduced mobility of the probes trapped in the glassy regions, appearing near the glass transition point. The average size of the glassy regions just below, and the strength of the infinite network formed upon the connection of the glassy regions above the glass transition point obey power law relations. The data around were interpreted on the basis of the percolation theory and we observed that the corresponding exponents and give static percolation values independent of the polymer composition.Received: 9 July 2004, Published online: 1 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 64.70.Pf Glass transitions - 82.35.Jk Copolymers, phase transitions, structure     

Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”

Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization |M|, susceptibility) and percolation cluster properties relating to the physical clusters, namely the Fortuin-Kasteleyn clusters (percolation probability P , percolation susceptibility _p, cluster size distributionn _l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, P being identical to |M| in the thermodynamic limit, while finite-size corrections differ. In contrast, _p differs from even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to, but not to _p. NearT _c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.     

The p + p → π+ + d reaction close to threshold at COSY

Differential and total cross sections of the p + p → π⁺ + d reaction close to threshold were measured employing a magnetic spectrograph with track reconstruction, a very thin liquid hydrogen target and an accelerated proton beam with high phase space density. The data resolve a previous discrepancy between the n + p → π⁰ + d and the π⁺ + d → 2p reaction close to threshold indicating that isospin symmetry may be broken in the s-wave part of the cross section.     

The NN → NNη reaction close to threshold

The pp → ppη and np → npη reactions at energies near the η production threshold are studied in a non-relativistic one boson exchange model, where the (1535 MeV) S11 resonance is excited through the exchange of π, η, ? and ω mesons and subsequently decays into an ηN pair. Energy integrated cross sections and energy spectra of the out going η's are reported. Providing NN and ηN final state interactions are taken into account coherently, the model reproduces both the scale and energy dependence of the cross section for the pp → ppη reactions up to 100 MeV. Final state interaction corrections due to the nucleon-nucleon and meson-nucleon forces influence strongly the scale and shape of the cross sections. The shape of the energy spectra of the outgoing η's provides a clear signature of the ηN force.     

On next-to-eikonal corrections to threshold resummation for the Drell–Yan and DIS cross sections

We study corrections suppressed by one power of the soft gluon energy to the resummation of threshold logarithms for the Drell–Yan cross section and for Deep Inelastic structure functions. While no general factorization theorem is known for these next-to-eikonal (NE) corrections, it is conjectured that at least a subset will exponentiate, along with the logarithms arising at leading power. Here we develop some general tools to study NE logarithms, and we construct an ansatz for threshold resummation that includes various sources of NE corrections, implementing in this context the improved collinear evolution recently proposed by Dokshitzer, Marchesini and Salam (DMS). We compare our ansatz to existing exact results at two and three loops, finding evidence for the exponentiation of leading NE logarithms and confirming the predictivity of DMS evolution.     

Electronic transition of C3H− in the vicinity of the lowest photodetachment threshold

The electronic spectrum of the C³H(D)^? anion has been studied near the lowest electron detachment threshold associated with the chain isomer. On the basis of the vibrational and rotational analyses, the photodetachment spectrum is assigned to the ³A″ ← [Xtilde]³A″ electronic transition of the cumulene-like C³H(D)^? anion. The spectrum is characterized by a rich vibrational structure leading to the determination of almost all fundamental frequencies. The vibrational progression involving the CCH(D) in plane bending mode (V¹ ₆) is fitted with a 1-dimensional potential energy curve along the CCH(D) angle. This fit and the rotational analysis enable the geometry of the upper state to be determined. Although this excited state is expected to have dipole bound character, its neutral counterpart has a significantly different structure. The observation of an excited triplet state near the electron detachment threshold and close to the the calculated transition state for the electron catalysed isomerization reaction leads to new insight into this process.