Related papers: A Non-Perturbative Approach to the Random-Bond Isi…
The $O(n)$ Gross-Neveu model for $n < 2$ presents a massless phase that can be characterized by right-left mover scattering processes. The limit $n \goto 0$ describes the on-shell properties of the random bond Ising model.
This is a non-perturbative treatment of correlation functions for the weakly coupled massless Gross-Neveu model in a finite volume. The main result is that all correlation functions, treated as distributions, are uniformly bounded in the…
We show how to perform systematically improvable variational calculations in the $O(2N)$ Gross-Neveu model for generic $N$, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the…
In this first paper we begin the application of variational methods to renormalisable asymptotically free field theories, using the Gross-Neveu model as a laboratory. This variational method has been shown to lead to a numerically…
The large N limit of the 3-d Gross-Neveu model is here studied on manifolds with positive and negative constant curvature. Using the $\zeta$-function regularization we analyze the critical properties of this model on the spaces $S^2 \times…
The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical…
The non-commutative O(N) Gross-Neveu model is solved in the large N limit in two and three space-time dimensions. The commutative version of the two dimensional model is a renormalizable quantum field theory, both in a coupling constant…
We examine the issue of renormalizability of asymptotically free field theories on non-commutative spaces. As an example, we solve the non-commutative O(N) invariant Gross-Neveu model at large N. On commutative space this is a…
We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is…
We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a…
We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass…
We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the…
The general prescription for constructing the continuum limit of a field theory is introduced. We then apply the prescription to construct the O(N) non-linear sigma model and the Gross-Neveu model in three dimensions using the large N…
We consider the Ginzburg-Landau MN-model that describes M N-vector cubic models with O(M)-symmetric couplings. We compute the renormalization-group functions to six-loop order in d=3. We focus on the limit N -> 0 which describes the…
We investigate the finite and large $N$ behaviors of independent-value O(N)-invariant matrix models. These are models defined with matrix-type fields and with no gradient term in their action. They are generically nonrenormalizable but can…
We propose a method to solve the Non Perturbative Renormalization Group equations for the $n$-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the $n$-point…
We reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…
We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which…
The aim of this paper is to investigate the non-relativistic limit of integrable quantum field theories with fermionic fields, such as the O(N) Gross-Neveu model, the supersymmetric Sinh-Gordon and non-linear sigma models. The…
This work is dedicated to the study of the noncommutative Gross-Neveu model. As it is known, in the canonical Weyl-Moyal approach the model is inconsistent, basically due to the separation of the amplitudes into planar and nonplanar parts.…