Quantum spherical XY model with orthorhombic anisotropy in two dimensions

The quantum spherical XY model with orthorhombic anisotropy is investigated. It is shown that in contradiction with the results of reference [#!9!#], the long-range magnetic order is stabilized in two dimensions. Both analytical and numerical results are presented. The incorrect results of the work [9] are explained to be the result of improper choice of quantization axis. Received 26 August 2002 / Received in final form 24 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: frid@tnu.crimea.ua     

Self-propelled particles with fluctuating speed and direction of motion in two dimensions

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.     

A spiral growth model for quasicrystals in two dimensions

Spiral space filling geometrical constructions using rhombuses in two dimensions are considered as plausible mechanisms for quasicrystal growth. These models will show staircase-like features which may be observed experimentally.     

Seven basic regimes of steady crystal growth in two dimensions

Using a Markov rate-process model, exact expressions are found for the steady growth rate of an edge of a two-dimensional crystal in terms of the numberM of particles along the edge, the height difference (or number of permanent steps)K along the edge, the nucleation rate , and the speed + of movement of steps. The familiar growth regimes can be identified with asymptotic regimes for the parametersK, (v/)^1/2, andM. From a mathematical viewpoint, there are seven basic regimes, of which the known physical regimes are special cases.     

Inversion relations,phase transitions and transfer matrix excitations for special spin models in two dimensions

The infrared and Raman active phonons (k=0) of orthorhombic TbF₃ and of isomorphous HoF₃ have been observed and attributed to the different irreducible representations of the factor groupD _2h. Moreover we investigated crystal-field excitations of the 4f-configuration of the Rare-Earth-ions and effects of their interaction with optical phonons, especially as a function of an external magnetic field. The infrared reflection spectra of these materials not only display reststrahlen bands of electric dipolar but also of magnetic dipolar type with a characteristic shape of the latter bands.On entering the ferromagnetic ordered state pertinent symmetry reductions (D _{2hC 2h}) become evident in the system of electronic transitions and optical phonons in TbF₃ by a change of selection rules and a magnetization-induced transfer of transition intensities to new components of the transition dipole or of the Raman polarizability tensor. These observations are in accordance with general symmetry considerations.The delocalization of the crystal-field excitations results in a Davydov splitting of the single-ion transitions.     

Diffusion generated motion for grain growth in two and three dimensions

An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grain boundaries are zero-level sets of signed distance functions. Curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains. Hundreds of thousands of grains can be simulated using a small number of signed distance functions (in this work, 32 in two dimensions and 64 in three dimensions are more than sufficient) using modest computational hardware.     

The collapse point of interacting trails in two dimensions from kinetic growth simulations

We present simulational evidence that kinetic growth trails on the square lattice are equivalent to interacting trails at their collapse temperature. As a consequence we give values for most of the canonical exponents of the trail collapse transition: these are significantly different from those proposed for interacting walks. We can also interpret our results in terms of the equivalent Lorentz lattice gas and find that this model does not display diffusion, as has been previously thought. Rather, the mean square displacement grows ast logt in timet.     

Critical interface in two dimensions

The interface separating two-dimensional phases close to a critical point is observed in the ferroelectric BaZr_xTi_1−xO₃ by transmission electron microscopy. The temperature dependence of the interfacial thickness is determined and compared with theoretical predictions.     

Classical molecules in two dimensions

The ground-state configurations and spectrum of two parallel two-dimensional classical atoms are obtained as a function of the inter-atomic distance ( ). The classical particles are confined by parabolic potentials and repel each other through a Coulomb potential. As a function of we find several configurational transitions which are of first or second order. For first- (second-) order transitions the first (second) derivative of the energy with respect to is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (softening of a mode). In the limit of an infinite number of electrons the Wigner bilayer system is recovered which moves through five different stable crystalline phases as a function of . For unequal strength of parabolic confinement we find that the number of configurational transitions increases.     

Quantum censorship in two dimensions

It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.     

Non-translation-invariant states in two dimensions

We construct a class of models with translation-invariant interaction for which in dimension two there already exist non-periodic Gibbs states at low temperatures.     

Dilaton gravity in two dimensions

The study of general two-dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important examples of spherically symmetric Black Holes, together with string inspired models, belong to this class, valuable knowledge can also be gained for these systems in the quantum case. In the last decade, new insights regarding the exact quantization of the geometric part of such theories have been obtained. They allow a systematic quantum field theoretical treatment, also in interactions with matter, without explicit introduction of a specific classical background geometry. The present review tries to assemble these results in a coherent manner, putting them at the same time into the perspective of the quite large literature on this subject.     

Supersymmetry anomally in two dimensions

In two dimensions we obtain a supersymmetric extension of a gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We also obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies.