Related papers: Some new exact critical-point amplitudes
The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the…
Studies of non-Fermi liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large-N approach to analyze an SU(N)xSU($\kappa N$) generalization of the model. We establish…
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…
A discrete gradient model for interfaces is studied. The interaction potential is a non-convex perturbation of the quadratic gradient potential. Based on a representation for the finite volume Gibbs measure obtained via a renormalization…
A fundamental result relevant to spin chains and two-dimensional disordered systems is that the sphere sigma model with instanton coupling theta=pi has a non-trivial low-energy fixed point and a gapless spectrum. This result is extended to…
In N=1 supersymmetric SO(N)/USp(2N) gauge theories with the tree-level superpotential W(\Phi) that is an arbitrary polynomial of the adjoint matter \Phi, the massless fluctuations about each quantum vacuum are described by U(1)^n gauge…
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In…
In this paper we consider classical and quantum versions of the critical long-range $O(N)$ model, for which we study finite-size and finite-temperature effects, respectively, at large $N$. First, we consider the classical (isotropic) model,…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
We consider new models of dark energy with finite time future singularities, by introducing the pressure density as a function of the scale factor. This approach gives acceptable phenomenological models of dark energy, practically…
Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit…
We compute the large $N$ effective action of the $O(N+1)/O(N)$ non-linear sigma model including the effect of the pion mass to order $m^2_{\pi}/f_{\pi}^2$. This action is more complex than the one corresponding to the chiral limit not only…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at…
The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $\sigma$ models are studied on $R^2 \times S^1$. The $N$-components scalar fields of the models are supposed to acquire a phase $e^{i2\pi\delta}$ $(0\leq \delta <1)$, along the circulation of the…
We study finite size effects in a family of systems in which a parameter controls interaction-range. In the long-range regime where the infinite-size free energy is universal, we show that the finite size effects are not universal but…
In the high energy limit of scattering amplitudes in Quantum Chromodynamics and supersymmetric theories the dominant Feynman diagrams are characterized by a hidden integrability. A well-known example is that of Odderon exchange, which can…
We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(\phi^i \phi^i)^2$. For $2<d<4$ these theories flow to the Wilson-Fisher fixed points for any $N$. A standard large $N$ Hubbard-Stratonovich…
The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional $\phi^4$ model serves as an example where a nontrivial low energy scaling regime is…
Form Factor Perturbation Theory is applied to study the spectrum of the O(3) non--linear sigma model with the topological term in the vicinity of $\theta = \pi$. Its effective action near this value is given by the non--integrable double…