De Polsi, Gonzalo Tissier, Matthieu Wschebor, Nicolás

It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated vector operator, invariant under all internal symmetries of the model, with scaling dimension $-1$. In this article, we compute the scaling dimensions of vector operator...

Panov, Yu. D. Moskvin, A. S. Ulitko, V. A. Chikov, A. A.
Published in
Physics of the Solid State

AbstractWe have treated a two-dimensional spin-pseudospin model, which generalizes a diluted antiferromagnetic Ising model with charged nonmagnetic impurities in the case of two types of charges. The analytical results in the Bethe approximation are compared with the results of numerical simulation using the classical Monte Carlo method for various...

Balog, Ivan Chaté, Hugues Delamotte, Bertrand Marohnic, Maroje Wschebor, Nicolás

We provide analytical arguments showing that the non-perturbative approximation scheme to Wilson's renormalisation group known as the derivative expansion has a finite radius of convergence. We also provide guidelines for choosing the regulator function at the heart of the procedure and propose empirical rules for selecting an optimal one, without ...

Zhou, Wei

The interfaces in the percolation and Ising models play an important role in the understanding of these models and are at the heart of several problematics: the Wulff construction, the mean curvature motion and the SLE theory. In his famous 1972 paper, Roland Dobrushin showed that the Ising model in dimensions d ≥ 3 has a Gibbs measure which is not...

Meneses, Simão Penedones, João Rychkov, Slava Viana Parente Lopes, J.M. Yvernay, Pierre

How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -- a non-conserved vector operator of dimension exactly $(d-1)$, whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via la...

Fytas, Nikolaos G. Martín-Mayor, Víctor Parisi, Giorgio Picco, Marco Sourlas, Nicolas

We provide a non-trivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional disordered system with some other correlation functions in a D-2 clean system. We first show how to check thes...

Tokar, V.I.

A self-consistent renormalization scheme suitable for the calculation of non-universal quantities in $n$-vector models with pair spin interactions of arbitrary extent has been suggested. The method has been based on the elimination of the fluctuating field components within the layers defined by the layer-cake representation of the propagator. The ...

Can, Van Hao

In a recent paper [15], Giardinà, Giberti, Hofstad, Prioriello have proved a law of large number and a central limit theorem with respect to the annealed measure for the magnetization of the Ising model on some random graphs including the random 2-regular graph. We present a new proof of their results, which applies to all random regular graphs. In...

Helali, Amine

Les méthodes de Monte Carlo par chaines de Markov MCMC sont des outils mathématiques utilisés pour simuler des mesures de probabilités π définies sur des espaces de grandes dimensions. Une des questions les plus importantes dans ce contexte est de savoir à quelle vitesse converge la chaine de Markov P vers la mesure invariante π. Pour mesurer la vi...

Marinazzo, Daniele Angelini, L. Pellicoro, M. Stramaglia, S.