arXiv subjects

Omar Abdelghani

Publications and source records attributed to Omar Abdelghani.

5 recordsLinked to original sources

arXiv2026

Log-Sobolev inequality for the sinh-Gordon model

For the sinh-Gordon model (without external mass term), we show that the log-Sobolev inequality holds uniformly in the lattice and volume regularisations for all parameters in the regime in which the Gaussian multiplicative chaos has second moments. As a consequence, this establishes that infinite-volume (massless) sinh-Gordon measures on $\mathbb{R}^2$ exist. The proof uses the Polchinski equation method for log-Sobolev inequalities. The required estimates on the renormalised potential are established using simple perturbation theoretic bounds, valid for absolutely monotone potentials, and an extension of the correlation inequality of Ding--Song--Sun to potentials in the GHS class. This inequality is proved also by using a variant of the Polchinski equation through the maximum principle.

math.PR↗

arXiv2026

The Ding-Song-Sun inequality for a class of even ferromagnets

Ding-Song-Sun proved the remarkable correlation inequality that the truncated two-point correlation function of ferromagnetic Ising models with arbitrary mixed-sign external field is largest when the field vanishes. This inequality has various important consequences such as log-Sobolev inequalities for Ising and $φ^4$ models up to and at the critical point. We extend the DSS inequality to the class of single spin measures satisfying the GHS condition. This is an important ingredient in our proof of the log-Sobolev inequality for the massless sinh-Gordon model on $\mathbb{R}^2$ in a forthcoming article.

math.PR↗

arXiv2026

Mass gap for the hierarchical sinh-Gordon model

The (massless) sinh-Gordon model is defined in terms of a continuum massless Gaussian free field perturbed by a cosh interaction. For the hierarchical version of the model, we prove existence of the infinite volume limit, a uniform log-Sobolev inequality, and a mass gap. Our results hold for all $b^2 \in (0,1)$ and simplify for $b^2 \in (0,1/2)$ for which the Gaussian multiplicative chaos has two moments. In an appendix, our renormalization group analysis is compared with the conjectures and controversies in physics which are mostly based on formal analytic continuation of conjectures for the sine-Gordon model and we raise some questions.

math.PR↗

arXiv2024

Topological quantum walk in synthetic non-Abelian gauge fields

We theoretically introduce synthetic non-Abelian gauge fields for topological quantum walks. The photonic mesh lattice configuration is generalized with polarization multiplexing to achieve a four-dimensional Hilbert space, based on which we provide photonic building blocks for realizing various quantum walks in non-Abelian gauge fields. It is found that SU(2) gauge fields can lead to Peierls substitution in both momenta and quasienergy. In one and two dimensions, we describe detailed photonic setups to realize topological quantum walk protocols whose Floquet winding numbers and Rudner-Lindner-Berg-Levin invariants can be effectively controlled by the gauge fields. Finally, we show how non-Abelian gauge fields facilitate convenient simulation of entanglement in conjunction with polarization-dependent and spatial-mode-dependent coin operations. Our results shed light on the study of synthetic non-Abelian gauge fields in photonic Floquet systems.

physics.optics↗

arXiv2023

Geometric Derivation of the Finite $N$ Master Loop Equation

In this paper we provide a geometric derivation of the master loop equation for the lattice Yang-Mills model with structure group $G \in \{SO(N),SU(N), U(N)\}$. This approach is based on integration by parts on $G$. In the appendix we compare our approach to that of \cite{Ch19a} and \cite{J16} based on Schwinger-Dyson equations, and \cite{SheSmZh22} based on stochastic analysis. In particular these approaches are all easily seen to be equivalent. The novelty in our approach is the use of intrinsic geometry of $G$ which we believe simplifies the derivation.

math-ph↗