Phase diagrams of U(1) lattice Higgs models

Phase diagrams for charge-one and charge-two scalar particles in compact QED are constructed using Monte Carlo methods on the ICL DAP computer. The results are in agreement with the features predicted by Fradkin and Shenker and with known and new limiting cases.     

Phase diagrams and cluster expansions for low temperatureP(φ)2 models

We give a cluster expansion for the Schwinger functions of the stable phases found in Part I. The Wightman axioms, the mass gap, and asymptoticity of perturbation theory follow.Supported in part by the National Science Foundation under Grant No. PHY 79-16812National Science Foundation predoctoral fellow, 1979–80. Currently Junior Fellow, Harvard University Society of Fellows     

Phase diagrams in nonlocal Polyakov-Nambu-Jona-Lasinio models constrained by lattice QCD results

Based on lattice QCD-adjusted SU(2)f nonlocal Polyakov-Nambu-Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.     

Phase diagrams and surface properties of modified water models

The surface properties and phase diagrams are examined for a number of modified water models. In the ‘bent’ family of models where the bond angle is decreased and the network structure is lost the surface tension is lower than in SPC/E water and the critical temperature is lower. In the ‘hybrid’ family of models which are hybrids between SPC/E water and a Lennard–Jones liquid the surface tension and the critical temperature are higher that in SPC/E water. These properties correlate well with the varying ability of the liquids to dissolve hard spheres. The surface potential, on the other hand, is slightly smaller in magnitude in the hybrid models than in SPC/E water because there is slightly less alignment of the dipoles in the surface layer. The degree of molecular alignment in the surface and the consequent surface potential drop is much lower in magnitude in the bent models than in SPC/E water.     

Phase diagrams of transition metals and the pseudopotential method

Phase stability boundaries for transition metals are derived from the condition of electron spectrum degeneration with respect to an external field.     

Phase boundary of the square-lattice Ising antiferromagnet by real space renormalization group methods

The transition temperature of the square lattice Ising antiferromagnet at finite magnetic field is calculated by three different approximations within the real space renormalization group approach. The most refined approximation is an extension of Kadanoff's potential moving method to a larger cell-size. The results of this approximation are in good agreement with recent Monte Carlo simulations and the Müller-Hartmann/Zittartz conjecture for the phase boundary.     

Phase diagrams of decomposing nanoalloys

The thermodynamics of nucleation and decomposition in small isolated particles are considered. There exist three possibilities: phase separation, prohibition of decomposition and a metastable state. We investigate the peculiarities of phase diagrams related to depletion of the nanosize parent phase even at the nucleation stage. For small particles the equilibrium diagram becomes split (and shifted and size dependent). Concentration, size and temperature hystereses take place. Size-dependent ‘critical supersaturation’, increasing with decreasing size, has been analysed.     

Phase diagrams of magnetic nanotubes

Analytical expressions for the total magnetic energy of two characteristic internal configurations of nanometric tubes are calculated. A magnetic phase diagram with respect to the aspect ratio of the tubes is obtained which allows a discussion about the possibility of getting ensembles of nanotubes with low coercive fields. A comparison with recently reported coercive fields of three different cobalt nanotube arrays agrees well with the phase diagram derived here.     

Unitary representations of the quantum group SU q (1,1): Structure of the dual space ofU q (sl(2))

Real forms of the quantum universal enveloping algebraU _q (sl(2)) and a topological quantum group associated with this algebra are discussed.     

SU(2) q in a Hilbert space of analytic functions

The algebraSU(2) _q is realized in a Hilbert spaceH _q ² of analytic functions; the starting point is the differential realization of operators that satisfyq-algebra in a Hilbert spaceH _q. The Weyl realization ofSU(2) _q is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2×2 linear representation ofSU(2) _q is obtained as consistency conditions for couplingj1=j2=1/2 toj=0, 1; the derivation of Clebsch-Gordan coefficients is sketched and theq-generalization of the rotation matrices is included. The unitary correspondence ofH _q with a Hilbert space of complex functions of a real variable is also studied. The study presented in this paper follows Bargmann's formalism for the rotation group as closely as possible.     

SO q (n+1,n−1) as a real form of SO q (2n,ℂ)

Quantum pseudo-orthogonal groups SO _q (n+1,n–1) are defined as real forms of quantum orthogonal groups SO _q (n+1,n–1) by means of a suitable antilinear involution. In particular, the casen=2 gives a quantized Lorentz group.     

Signature of the ferromagnetic (T = 0) transition in real space and time

A detailed study of the spatio-temporal dynamics in several Hubbard clusters at zero temperature is performed. Small systems of two and three electrons, which could be considered representative systems of Nagaoka's, Mielke's and Tasaki's ferromagnetism, are investigated using a combination of analytical and numerical exact diagonalization techniques. The results raise the possibility that spin-dependent localization is correlated in real space and real time with the transition to a saturated ferromagnetic state. The long-time average of the expectation value of the center of mass coordinates for electrons with spin up does not coincide with that for electrons with spin down at the transition. The reason for this is that the long-time averages of the probabilities are different for states in which the spins of one system are exchanged with another. The physical origin of itinerant ferromagnetism is discussed.     

Phase diagrams of lyotropic cholesteric fluids

Experimental investigations of lyotropic cholesterics fluids are presented which show that changes in the shape anisotropy and chirality of the micellar population determine the topology of the temperature-concentration phase diagrams. For given amounts of the substances which induce the chirality and modify the shape anisotropy of the micelles, two distinct biaxial cholesteric phases are disclosed in the phase diagrams. This is interpreted in the framework of the catastrophe theory of phase transitions.     

Topological analysis of real space properties for the solid-state full-potential APW DFT method

For the solid-state density functional program Elk a module was developed that enables to interface the crystal orbitals data into the DGrid package. Within DGrid the real-space electronic properties, like the electron density and its gradient or Laplacian, kinetic energy density, electron localizability indicator, etc., are computed. The properties can be searched for critical points as well as for the interconnection lines between them. Additionally, the basins can be evaluated and the property integrals can be calculated. The results of topological analysis for fcc Al, MgB₂, CaTiO₃, and urea molecular crystal are discussed and compared with the experimental data. The role of certain computation parameters of (L)APW method is also analyzed.     

Phase diagrams of Ising models on Husimi trees. I. Pure multisite interaction systems

Lattice spin systems with multisite interactions have rich and interesting phase diagrams. We present some results for such systems involving Ising spins (=±1) using a generalization of the Bethe lattice approximation. First, we show that our approach yields good approximations for the phase diagrams of some recently studied multisite interaction systems. Second, a multisite interaction system with competing interactions is investigated and a strong connection with results from the theory of dynamical systems is made. We exhibit a full bifurcation diagram, chaos, period-3 windows, etc., for the magnetization of the base site of this system.