Facilitating online discussion, tutoring and moderating skills in clinical psychology lecturers

The inclusion of online approaches in clinical psychology training has necessitated an examination of the skills required by trainers. This paper describes the development of a short tutorial to promote online discussion tutoring and moderation skills in clinical psychology lecturers

Simulating non-commutative field theory

Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present numeric results for 2d NC gauge theory of rank 1, which turns out to be renormalizable. The area law for the Wilson loop holds at small area, but at large area we observe a rotating phase, which corresponds to an Aharonov-Bohm effect. Next we investigate the NC phi^4 model in d=3 and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns.Comment: 6 pages, 7 figures, Lattice2002(theoretical

Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension $d_H$ =1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. The topological effects become evident from the emergence of a logarithmic periodic oscillation superimposed to a power law in the decay of the magnetization and its logarithmic derivative and also from the dependence of the critical exponents on the segmentation step. These oscillations are discussed in the framework of the discrete scale invariance of the substrate and carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The exponent $\theta$ of the initial increase in the magnetization was also obtained and the results suggest that it would be almost independent of the fractal dimension of the susbstrate, provided that $d_H$ is close enough to d=2.Comment: 9 figures, 3 tables, 10 page

A magnetic model for the incommensurate I phase of spin-Peierls systems

A magnetic model is proposed for describing the incommensurate I phase of spin-Peierls systems. Based on the harmonicity of the lattice distortion, its main ingredient is that the distortion of the lattice adjusts to the average magnetization such that the system is always gapful. The presence of dynamical incommensurabilities in the fluctuation spectra is also predicted. Recent experimental results for CuGeO_3 obtained by NMR, ESR and light scattering absorption are well understood within this model.Comment: 8 pages, 3 figures, Latex with EPL style files all include

Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field

The T=0 dynamical properties of the one-dimensional (1D) $s=1/2$ Heisenberg antiferromagnet in a uniform magnetic field are studied via Bethe ansatz for cyclic chains of $N$ sites. The ground state at magnetization $0<M_z<N/2$, which can be interpreted as a state with $2M_z$ spinons or as a state of $M_z$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the {\em psinons} and {\em antipsinons}. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of lineshapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF$_3$, Cu(C$_4$H$_4$N$_2)(NO_3)_2$, and CuGeO$_3$.Comment: 13 pages, 12 figure

Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure

Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation

The anisotropic XXZ spin-1/2 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated thoughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Isinglike ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic correlation in the out-of-plane s_i^z component, at higher temperatures in the antiferromagnetic XXZ chain, dominantly at low temperatures in the ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain. We find that the converse effect also occurs in the antiferromagnetic XXZ chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in the s_i^xy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XY) anisotropy; (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.Comment: New results added to text and figures. 12 pages, 18 figures, 3 tables. Published versio

Dynamical correlation functions of the XXZ model at finite temperature

Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the following three limits: the static, the zero-temperature and the XY limits.Comment: 22 pages, v4: typos corrected, published versio

First Simulation Results for the Photon in a Non-Commutative Space

We present preliminary simulation results for QED in a non-commutative 4d space-time, which is discretized to a fuzzy lattice. Its numerical treatment becomes feasible after its mapping onto a dimensionally reduced twisted Eguchi-Kawai matrix model. In this formulation we investigate the Wilson loops and in particular the Creutz ratios. This is an ongoing project which aims at non-perturbative predictions for the photon, which can be confronted with phenomenology in order to verify the possible existence of non-commutativity in nature.Comment: 3 pages, 4 figures, talk presented by J. Volkholz at Lattice2004(theory