Related papers: Numerical study of the mass spectrum in the 2D O(3…
In this talk we will report on a study of the $\theta$-dependence of the string tension and of the mass gap of four-dimensional SU($N$) Yang--Mills theories. The spectrum at $N=3$ and $N=6$ was obtained on the lattice at various imaginary…
We use the 2-dimensional $\sigma$ model as a toy model to study the behavior of anomalous amplitudes in the limit where the constituent quark mass is small. Symmetry arguments tell that the $\pi^o\to\gamma$ amplitude should vanish if $m\to…
We report the results of a Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\sigma$ model. The notable finding is that it agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix ansatz…
An effective sigma model describing behavior of the 3d rigid string with a $\theta$-term at $\theta=\pi$ is proposed. It contains non-perturbative corrections resulting from summation over different genera of the 2d surfaces. The effective…
The two-point functions of the energy-momentum tensor and the Noether current are used to probe the O(3) nonlinear sigma model in an energy range below 10^4 in units of the mass gap $m$. We argue that the form factor approach, with the form…
Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disordered electron systems. They also occur in dimensionally reduced quantum gravity; recently they have been…
A review is given on the recently proposed two dimensional axion model (O(3) sigma-model with a dynamical Hopf-term) and the T-duality relating it to the SU(2)xU(1) symmetric anisotropic sigma-model. Strong evidence is presented for the…
Theory of strong decays defines in addition to decay widths, also the channel coupling and the mass shifts of the levels above the decay thresholds. In the standard decay models of the 3P0 type the decay vertex is taken to be a…
We use the presently observed number density of large X-ray clusters and linear mass power spectra to constrain the shape parameter ($\Gamma$), the spectral index ($n$), the amplitude of matter density perturbations on the scale of $8…
We investigate low-energy properties of the alternating spin chain model composed of spin $s_1$ and $s_2$ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3)…
The mass spectrum of the 3d 3-state Potts model is considered in the broken phase (a) near the second order Ising critical point in the temperature-magnetic field plane and (b) near the weakly first order transition point at zero magnetic…
The long-term goal of this project is the non-perturbative renormalization of the energy-momentum tensor in the 2d $O(3)$ non-linear sigma model using different methods which have been developed for QCD applications. As a first step, we…
I survey the kinds of critical behavior believed to be exhibited in two-dimensional disordered systems. I review the different replica sigma models used to describe the low-energy physics, and discuss how critical points appear because of…
A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are ``self-similar'' in being basically rescaled copies…
In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind…
We study the critical behavior of discrete spin models related to the 2d O(3) non-linear sigma model. Precise numerical results suggest that models with sufficiently large discrete subgroups are in the same universality class as the…
We study the O(3) sigma model in $D=2$ on the lattice with a Boltzmann weight linearized in $\beta$ on each link. While the spin formulation now suffers from a sign-problem the equivalent loop model remains positive and becomes particularly…
We present a new and exploratory approach to determine the $\Delta\beta(\beta)$-shift in the $O(3)$ nonlinear $\sigma$-model. The method is based on a scaling hypothesis for a free energy difference, which is assumed to be valid in a…
We present lattice results for simulations of the $O(3)$ non-linear sigma model at finite chemical potential. The complex action problem is overcome by a dual variable representation of the model. We discuss two aspects of the theory at…
Detecting and measuring repetitiveness of strings is a problem that has been extensively studied in data compression and text indexing. However, when the data are structured in a non-linear way, like in the context of two-dimensional…