Related papers: The two-phase issue in the O(n) non-linear $\sigma…
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…
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 investigate the O(N) symmetric linear $\sigma$-model in two dimensions by means of an exact nonperturbative evolution equation. The perturbative infrared divergences are absent in this formulation. We use a simple approximative solution…
By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough…
We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte Carlo update routine, blockspin transformations…
Using Monte Carlo simulations, we consider the lattice version of the $O(N)\otimes O(M)$ sigma model for $2\leq M\leq4$ and $M\leq N \leq8$. We find a continuous transition for $N\geq M+4$. Estimates of the critical exponents for cases of…
We study the two-dimensional XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and…
The O(n) non-linear $\sigma$-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such…
The action of the 2d O(3) non-linear sigma model on the lattice in a bath of particles, when expressed in terms of standard O(3) degrees of freedom, is complex. A reformulation of the model in terms of new variables that makes the action…
We construct the general O(N)-symmetric non-linear sigma model in 2+1 spacetime dimensions at the Lifshitz point with dynamical critical exponent z=2. For a particular choice of the free parameters, the model is asymptotically free with the…
We present complete three loop results and preliminary four loop results for the 2D O(n) nonlinear sigma model with 0-loop and 1-loop Symanzik improved actions. This calculation aims to test the improvement in the numerical precision that…
We have simulated the asymptotically free two-dimensional O(3) model at nonzero chemical potential using the model's dual representation. We first demonstrate how the latter solves the sign (complex action) problem. The system displays a…
We present a comprehensive numerical study of dynamic phase transitions in the two-dimensional kinetic Ising model under a non-antisymmetric time-dependent magnetic field including a sinusoidal term and a second harmonic component. We…
We use the half-filled zeroth Landau level in graphene as a regularization scheme to study the physics of the SO(5) non-linear sigma model subject to a Wess-Zumino-Witten topological term in 2+1 dimensions. As shown by Ippoliti et al. [PRB…
We present a dynamic Monte Carlo study of the Kosterlitz-Thouless phase transition for the spin-1/2 quantum XY model in two dimensions. The short-time dynamic scaling behaviour is found and the dynamical exponent $\theta$, $z$ and the…
We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $\sigma$-models. We then apply the method…
We discuss the feasibility of applying Diagrammatic Monte-Carlo algorithms to the weak-coupling expansions of asymptotically free quantum field theories, taking the large-$N$ limit of the $O(N)$ sigma-model as the simplest example where…
In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been found before with standard discretizations and lattice spacings. Here the situation is analyzed further employing additional data for the step scaling function of…
We discuss the thermodynamics of the O(3) nonlinear sigma model in 1+1 dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By…
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…