Braid matrices and structure constants for minimal conformal models

Using the Feigin-Fuchs representation of minimal conformal models in a form introduced recently by one of us, the braid group representation matrices, describing the analytic continuation properties of conformal blocks, are computed. In a suitable normalization, their matrix elements are shown to essentially factorize into pairs of Boltzmann weights of critical RSOS models in a certain limit of the spectral parameter. These Boltzmann weights are related to quantum groupR-matrices by the vertex-SOS transformation. We show that the crossing symmetry of the four-point function in left-right symmetric models follows from a quantum group relation, also called crossing symmetry. This observation gives a simple way to evaluate the structure constants.Supported by NSF grant DMS 8610730     

Ising models with interfaces,defect lines,and walls

The transverse fluctuations of meandering interfaces in two-dimensional SOS models containing walls and defect lines may lead to a singularity in the correlation function. Corresponding Ising models below the bulk critical temperature are studied using an exact analytical transfermatrix method and Monte Carlo simulations. Typically, a rather smooth behaviour is observed in static and dynamic quantities.     

Spherical conformal models for compact stars

We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints.     

Random resistor network model of minimal conductivity in graphene

Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.     

Random layered frustration models

We study inhomogeneous two-dimensional Ising models with a random distribution of ferro- and antiferromagnetic couplings,K _ij =±K, or equivalently a random distribution of frustrations. In particular, we considerRandom Layered Frustration models (RLF) where randomness is confined to the vertical direction. These RLF-models are solved exactly, i.e., partition function and free energy are obtained in closed form for an arbitrary random distribution of finite period. The phase transition is of Ising type. A simple formula for the transition temperature is derived which depends only on the mean coupling , but not on other details of the distribution. Both cases,T _c =0 andT _c 0, are possible. Groundstate energy and groundstate degeneracy, or equivalently the rest entropy, are determined. It is found that both the occurence or absence of a phase transition may be accompanied with vanishing or nonvanishing rest entropy. We also show that for the RLF-models a phase transition is excluded when all groundstates are connected with one another by local transformations which presumably holds generally. A remarkable result is that the transition of the ferromagnetic Ising model can be destroyed completely if one replaces an arbitrarily small fraction of ferromagnetic couplings by antiferromagnetic ones in a suitable way.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Synchronization defect lines in complex-oscillatory target waves

It is well known that one of key features of spiral waves in complex-oscillatory media is the appearance of synchronization defect lines, across which the phase of the oscillation changes by multiplies of 2π. In this Letter, we report the appearance of synchronization defect lines in target waves in complex-oscillatory media by studying a model of two-dimensional Rössler reaction-diffusion system subject to an appropriate periodic force in a small region of the center of domain. The geometric structure and stability of the defect lines are studied.     

Topological defect solutions in the spherically symmetric space-time admitting conformal motion

In this paper, we have examined strings with monopole and electric field and domain walls with matter and electric field in the spherically symmetric space-time admitting a one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for a spherically symmetric space-time via conformal motions. Also, we have discussed the features of the obtained solutions.     

Chiral partition functions characterizing rational conformal models

Rational conformal theories are characterized by a chiral (analytic in the modular parameter) “partition function” with values in the fusion rules algebra covariant with respect to a subgroup of the modular group.     

Level-rank duality of WZW models in conformal field theory

We consider the decomposition of the conformal blocks under the conformal embeddings. The case (â is an affine extension of the abelian subalgebra of the central elements ofgl(lr)) is studied in detal. The reciprocal decompositions of -modules induce a pairing between the spaces of conformal blocks of and Wess-Zumino-Witten models on the Riemann sphere. The completeness of the pairing is shown. Hence it defines aduality between two spaces.Dedicated to Professor Masahisa Adachi on his 60th birthday     

Metastates in disordered mean-field models: Random field and hopfield models

We rigorously investigate the size dependence of disordered mean-field models with finite local spin space in terms of metastates. Thereby we provide an illustration of the framework of metastates for systems of randomly competing Gibbs measures. In particular we consider the thermodynamic limit of the empirical metastate , whereμ _n (η) is the Gibbs measure in the finite volume {1,…,n} and the frozen disorder variableη is fixed. We treat explicitly the Hopfield model with finitely many patterns and the Curie-Weiss random field Ising model. In both examples in the phase transition regime the empirical metastate is dispersed for largeN. Moreover, it does not converge for a.e.η, but rather in distribution, for whose limits we given explicit expressions. We also discuss another notion of metastates, due to Aizenman and Wehr.     

The defect character of interface junction lines

Junction lines, where three or more interfaces meet in polycrystalline materials, are analysed from a topological point of view. Using circuit mapping methods, it is shown that, in contiguous polyerystals, the dislocations constituting the interfaces always react at junctions according to topological conservation principles. This conclusion is at variance with recent suggestions in the literature. In addition, it is shown that, in certain circumstances, junction lines can themselves exhibit defect character, i.e., dislocation and/or disclination character. Such defects arise in order to accommodate the coexistence of the abutting crystals. Simple examples are illustrated.     

Ramond sector of the supersymmetric minimal models

A Coulomb gas representation for the Ramond sectors of the N = 1 supersymmetric models is constructed. The fusion rules and the 4-point functions for the Ramond fields are calculated explicitly by this method and used to describe the Z₂ odd sectors of the tricritical Ising model and of the critical Kosterlitz-Thouless XY model.     

Spontaneous parity violation and minimal Higgs models

In this paper we present a model for the spontaneous breaking of parity with two Higgs doublets and two neutral Higgs singlets which are even and odd under -parity. The condition can be satisfied without introducing bidoublets, and it is induced by the breaking of -parity through the vacuum expectation value of the odd Higgs singlet. Examples of left–right symmetric and mirror fermions models in grand unified theories are presented. PACS 12.60.Cn; 14.80.Cp; 12.10.Dm