Related papers: A Non-Perturbative Approach to the Random-Bond Isi…
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to…
The Gross-Neveu model in 1+1 dimensions is generalized to the case of different scalar and pseudoscalar coupling constants. This enables us to interpolate smoothly between the standard massless Gross-Neveu models with either discrete or…
The O$(N)$ vector model in the presence of a boundary has a non-trivial fixed point in $(4-\epsilon)$ dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is…
Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large N features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as…
We show that the noncommutativity of space-time destroys the renormalizability of the 1/N expansion of the O(N) Gross-Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the…
The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant scalar field theories in $d$ dimensions is studied by applying the $1/N$ expansion and strong coupling analysis. The $O(1/N)$ correction to the $\beta$-function…
We present a calculation of the three-point functions of the O(N)-symmetric sigma model. The calculation is done nonperturbatively by means of a higher-order 1/N expansion combined with a tachyonic regularization which we proposed in…
A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive…
We introduce some techniques to investigate dynamical mass generation. The Gross-Neveu model (GN) is used as a toy model, because the GN mass gap is exactly known, making it possible to check reliability of the various methods. Very…
We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the…
We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of…
We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…
It was recently shown [Phys. Rev. Lett. {\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming…
We investigate the high energy behavior of the SU(N) chiral Gross-Neveu model in 1 + 1 dimensions. The model is integrable and matrix elements of several local operators (form factors) are known exactly. The form factors show rapidity space…
We study the non-commutative matrix model which arises as the low-energy effective action of open strings in WZW models. We re-derive this fuzzy effective gauge dynamics in two different ways, without recourse to conformal field theory. The…
We study the critical bosonic O(N) vector model with quenched random mass disorder in the large N limit. Due to the replicated action which is sometimes not bounded from below, we avoid the replica trick and adopt a traditional approach to…
This paper is concerned with the energy decomposition of various nonlocal models, including elasticity, thin plates, and gradient elasticity, to arrive at bond-based nonlocal models in which the bond force depends only on the deformation of…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
We analyze the renormalization group fixed point of the two-dimensional Ising model at criticality. In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed…
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…