相关论文: New Universality Classes in One--Dimensional $O(N)…
Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…
It was recently found that the classical 3d O$(N)$ model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as $\langle \vec{S}(x)…
In this work, we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular, we study how nonreciprocal coupling between two $O(n_i)$ order parameters (with $i=1,2$) affects the…
Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with non-equilibrium problems, however, the distinction in…
We study a classical spin model (more precisely a class of models) with O(N) symmetry that can be viewed as a simplified $D$ dimensional lattice model. It is equivalent to a non-translationinvariant one dimensional model and contains the…
We investigate the low-temperature behavior of two-dimensional (2D) RP$^{N-1}$ models, characterized by a global O($N$) symmetry and a local ${\mathbb Z}_2$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
In these lecture notes prepared for the 11th Taiwan Spring School, Taipei 1997}, and updated for the Saalburg summer school 1998, we review the solutions of O(N) or U(N) models in the large N limit and as 1/N expansions, in the case of…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
The 1/N expansion of the two-particle irreducible (2PI) effective action is employed to compute universal properties at the second-order phase transition of an O(N)-symmetric N-vector model directly in three dimensions. At next-to-leading…
The critical behavior of the random field $O(N)$ model driven at a uniform velocity is investigated at zero-temperature. From naive phenomenological arguments, we introduce a dimensional reduction property, which relates the large-scale…
The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with…
Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking…
We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for D->1, while N->0 leads to self-avoiding tethered membranes (as the O(N) model reduces to…
We discuss general theories of N scalar fields with O(N) symmetry. In addition to the standard case of linearly realized symmetry there are also examples that carry nonlinear realizations, with the topology of a cylinder $R\times S^{N-1}$…
A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central limit theorem show that the model belongs to the universality…
We consider the critical behaviour of long-range $O(n)$ models ($n \ge 0$) on ${\mathbb Z}^d$, with interaction that decays with distance $r$ as $r^{-(d+\alpha)}$, for $\alpha \in (0,2)$. For $n \ge 1$, we study the $n$-component…
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…