相关论文: New Universality Classes for Two-Dimensional $\sig…
In this paper, we provide an invariant formulation of completely integrable $CP^{N-1}$ Euclidean sigma models in two dimensions defined on the Riemann sphere $S^2$. The scaling invariance is explicitly taken into account by expressing all…
We construct a qubit regularization of the $O(3)$ non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldline formulation and worm algorithms, we show that in…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
We analyze universal and nonuniversal finite-size effects of lattice systems in a $L^d$ geometry above the upper critical dimension d = 4 within the O(n) symmetric $\phi^4$ lattice theory. On the basis of exact results for $n \to\infty$ and…
We study \theta-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do…
We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably…
We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various…
We prove the universality of predictions for linear perturbations from the entire class of models of inflation driven by a pseudo-scalar field coupled to an SU($N$) gauge boson, where SU($2$) subgroups in the SU($N$) crossed with the…
We discuss the two-dimensional Grassmannian sigma model $\mathbb{G}_{N, M}$ on a finite interval $L$. The different boundary conditions which allow to obtain analytical solutions by the saddle-point method in the large $N$ limit are…
The low-energy limits of models with disorder are frequently described by sigma models. In two dimensions, most sigma models admit either a Wess-Zumino-Witten or a theta term. When such a term is present the model can have a stable critical…
For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are:…
We classify four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories with a simple gauge group admitting a large $N$ limit that flow to non-trivial superconformal fixed points in the infrared. We focus on the cases where the large $N$…
Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions $d \geq 2$. While the ferro- and antiferromagnetic models are essentially equivalent, the…
We investigate a two-dimensional classical $-vector model with a generic nearest-neighbor interaction $W(\bsigma_i\cdot \bsigma_j)$ in the large-N limit, focusing on the finite-temperature transition point at which energy-energy…
I propose a class of D\geq{2} lattice SU(N) gauge theories dual to certain vector models endowed with the local [U(N)]^{D} conjugation-invariance and Z_{N} gauge symmetry. In the latter models, both the partitition function and Wilson loop…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions. They are tightly linked to the monotone cellular automata called bootstrap percolation. Among the three classes of such…
In the context of integrable field theory with boundary, the integrable non-linear sigma models in two dimensions, for example, the $O(N)$, the principal chiral, the ${\rm CP}^{N-1}$ and the complex Grassmannian sigma models are discussed…
The nonuniversal behavior of two noncompact nonlinear sigma models is described. When these theories are defined on a lattice, the behavior of the order parameter (magnetization) near the critical point is sensitive to the details of the…
The critical behavior of two-dimensional ${\rm O}(N)$ $\sigma$ models with $N\leq 2$ on the square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green's…