Finite-temperature phase transitions in the quantum fully frustrated Ising models

The quantum antiferromagnetic spin-1/2 Ising model on a triangular lattice and analogous fully frustrated Ising model on a square lattice with quantum fluctuations induced by the application of the transverse magnetic field are studied at finite temperatures by constructing an exact mapping onto a purely classical model with a more complex interaction. It is shown that in weak fields the temperatures of the phase transitions separating the critical phase from the ordered and disordered phases in both models are proportional to the magnitude of the field.Comment: 5 pages, RevTex

Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a strong magnetic field and a smooth random potential with correlation length Lambda and amplitude Delta. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. In accordance with the experimental situation, Lambda is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function varepsilon(omega,q) to describe the effect of screening on the electron-phonon coupling. In the low temperature, high frequency regime T << Delta (omega_q*Lambda /v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q) are independent of temperature. The classical percolation indices give alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW occurs is found to be given by the scaling law |Delta \bar{\nu}| approx (omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon coupling and the screening due to the 2DEG on the filling factor leads to a double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad

Thermohydrodynamics in Quantum Hall Systems

A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the local equilibrium are described by the equations of conservation with the number and thermal-energy flux densities. A model of these flux densities due to hopping and drift processes is introduced for a random potential varying slowly compared to both the magnetic length and the phase coherence length. The flux measured in the standard transport experiment is derived and is used to define a transport component of the flux density. The equations of conservation can be written in terms of the transport component only. As an illustration, the theory is applied to the Ettingshausen effect, in which a one-dimensional spatial variation of the electron temperature is produced perpendicular to the current.Comment: 10 pages, 1 figur

Scaling Theory of the Integer Quantum Hall Effect

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys

Development of mandibular, hyoid and hypobranchial muscles in the zebrafish: homologies and evolution of these muscles within bony fishes and tetrapods

<p>Abstract</p> <p>Background</p> <p>During vertebrate head evolution, muscle changes accompanied radical modification of the skeleton. Recent studies have suggested that muscles and their innervation evolve less rapidly than cartilage. The freshwater teleostean zebrafish (<it>Danio rerio</it>) is the most studied actinopterygian model organism, and is sometimes taken to represent osteichthyans as a whole, which include bony fishes and tetrapods. Most work concerning zebrafish cranial muscles has focused on larval stages. We set out to describe the later development of zebrafish head muscles and compare muscle homologies across the Osteichthyes.</p> <p>Results</p> <p>We describe one new muscle and show that the number of mandibular, hyoid and hypobranchial muscles found in four day-old zebrafish larvae is similar to that found in the adult. However, the overall configuration and/or the number of divisions of these muscles change during development. For example, the undivided adductor mandibulae of early larvae gives rise to the adductor mandibulae sections A0, A1-OST, A2 and Aω, and the protractor hyoideus becomes divided into dorsal and ventral portions in adults. There is not always a correspondence between the ontogeny of these muscles in the zebrafish and their evolution within the Osteichthyes. All of the 13 mandibular, hyoid and hypobranchial muscles present in the adult zebrafish are found in at least some other living teleosts, and all except the protractor hyoideus are found in at least some extant non-teleost actinopterygians. Of these muscles, about a quarter (intermandibularis anterior, adductor mandibulae, sternohyoideus) are found in at least some living tetrapods, and a further quarter (levator arcus palatini, adductor arcus palatini, adductor operculi) in at least some extant sarcopterygian fish.</p> <p>Conclusion</p> <p>Although the zebrafish occupies a rather derived phylogenetic position within actinopterygians and even within teleosts, with respect to the mandibular, hyoid and hypobranchial muscles it seems justified to consider it an appropriate representative of these two groups. Among these muscles, the three with clear homologues in tetrapods and the further three identified in sarcopterygian fish are particularly appropriate for comparisons of results between the actinopterygian zebrafish and the sarcopterygians.</p