Related papers: Large N limit of O(N) vector models
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…
We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the…
The self-energy of the critical 3-dimensional O(N) model is calculated. The analysis is performed in the context of the Non-Perturbative Renormalization Group, by exploiting an approximation which takes into account contributions of an…
We study operators in the sl(2) sector of N=4 SYM in the generalised scaling limit, where the spin is large and the length of the operator scales with the logarithm of the spin. At leading order in the large spin expansion the scaling…
We analyze the long distance behavior of the two-point functions for an interacting scalar $O(N)$ model in de Sitter spacetime. Following our previous work, this behavior is analyzed by analytic continuation of the Euclidean correlators,…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
Tensor models generalize matrix models and generate colored triangulations of pseudo-manifolds in dimensions $D\geq 3$. The free energies of some models have been recently shown to admit a double scaling limit, i.e. large tensor size $N$…
The thermodynamic limit of certain exponential corrections to the weak coupling expansion of two-dimensional models is investigated. The expectation values of operators contributing to the first order coefficient of the low-temperature…
A derivative expansion of the Wegner-Houghton equation is derived for a scalar theory. The corresponding full non-perturbative renormalization group equations for the potential and the wave-function renormalization function are presented.…
We motivate inflationary scenarios with many scalar fields, and give a complete formulation of adiabatic and entropy perturbations. We find that if the potential is very flat, or if the theory has a SO(N) symmetry, the calculation of the…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
We derive the double scaling limit of eigenvalue correlations in the random matrix model at critical points and we relate the limiting correlation functions to a nonlinear hierarchy of ordinary differential equations.
We study the large $N$ limit of $O(N)$ scalar field theory with classically marginal $\phi^6$ interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large $N$. We find…
Motivated by the problem of thermalization in heavy-ion collisions, we present numerical simulations of the nonequilibrium evolution of the O(N) model in 1+2 dimensions with longitudinal expansion and in the presence of a background field.…
We study higher-order small-noise fluctuation expansions for the overdamped Langevin dynamics in a quartic double-well potential. Assuming that the initial data admits a suitable expansion structure, we obtain a strong dynamical expansion…
We present direct representations of the scaling functions of the 3d O(4) model which are relevant for comparisons to other models, in particular QCD. This is done in terms of expansions in the scaling variable z=t/h^{1/\beta\delta}. The…
We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum…
The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both…
The two-dimensional one-component plasma is an ubiquitous model for several vortex systems. For special values of the coupling constant $\beta q^2$ (where $q$ is the particles charge and $\beta$ the inverse temperature), the model also…
We investigate $O(N)$-symmetric vector field theories in the double scaling limit. Our model describes branched polymeric systems in $D$ dimensions, whose multicritical series interpolates between the Cayley tree and the ordinary random…