Related papers: Absence of Asymptotic Freedom in Non-Abelian Model…
We investigate the percolation properties of equatorial strips in the two-dimensional O(3) nonlinear $\sigma$ model. We find convincing evidence that such strips do not percolate at low temperatures, provided they are sufficiently narrow.…
We present the results of a numerical investigation of percolation properties in a version of the classical Heisenberg model. In particular we study the percolation properties of the subsets of the lattice corresponding to equatorial strips…
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…
We conducted Monte Carlo simulations to analyze the percolation transition of a non-symmetric loop model on a regular three-dimensional lattice. We calculated the critical exponents for the percolation transition of this model. The…
We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the…
We consider the classical XY model (O(2) nonlinear sigma-model) on a class of lattices with the (fractal) dimensions 1<D<2. The Berezinskii's harmonic approximation suggests that the model undergoes a phase transition in which the low…
The linear O($N$) sigma model undergoes a symmetry restoring phase transition at finite temperature. We show that the nonlinear O($N$) sigma model also undergoes a symmetry restoring phase transition; the critical temperatures are the same…
An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $O(3)$ non-linear $\sigma$-model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We…
We consider a two-dimensional $\sigma$-model with discrete icosahedral/dodecahedral symmetry. Using the perturbative renormalization group, we argue that this model has a different continuum limit with respect to the O(3) $\sigma$ model.…
Phase transitions in isotropic quantum antiferromagnets are described by an O(3) nonlinear quantum field theory. In three dimensions, the fundamental property of this theory is logarithmic scaling of the coupling constant. At the quantum…
We consider the Edwards-Anderson Ising Spin Glass model for non negative temperatures T: We define the natural notion of Boltzmann- Gibbs measure for the Edwards-Anderson spin glass at a given temperature, and of unsatisfied edges. We prove…
In this paper we construct non-Abelian gauge theories with fermions and scalars that nevertheless possess asymptotic freedom.The scalars are taken to be in a chiral multiplet transforming as $(2,2)$ under $SU(2)_L\otimes SU(2)_R$ and…
The classical Heisenberg model is one of the most fundamental models in statistical and condensed matter physics. Extensive theoretical and numerical studies suggest that, in two dimensions, this model does not exhibit a finite-temperature…
Using high statistic numerical results we investigate the properties of the O(3) non-linear 2D sigma-model. Our main concern is the detection of an hypothetical Kosterlitz-Thouless-like (KT) phase transition which would contradict the…
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial…
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…
Internal friction and speed of sound of a-SiO(2) was measured above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, non-linear effects, and clamping losses. Strain amplitudes e(A) = 10^{-8} mark the…
We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our…
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 analytically solve the zero-temperature dynamics of the spherical model with non-reciprocal random interactions drawn from the real elliptic ensemble of random matrices, where a single parameter $\eta$ continuously interpolates between…