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In this paper we analyze in detail the next-to-leading order (NLO) of the recently obtained large $N$ expansion for the multi-orientable (MO) tensor model. From a combinatorial point of view, we find the class of Feynman tensor graphs…

High Energy Physics - Theory · Physics 2015-03-30 Matti Raasakka , Adrian Tanasa

We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values…

High Energy Physics - Theory · Physics 2023-04-12 Marten Reehorst , Maria Refinetti , Alessandro Vichi

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

Dynamical Systems · Mathematics 2008-05-16 Claudio Bonanno , Stefano Isola

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the…

High Energy Physics - Theory · Physics 2010-04-05 J. Balog , P. Weisz

We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original…

Probability · Mathematics 2016-08-16 Pierre Del Moral , Frédéric Patras , Sylvain Rubenthaler

A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect…

Condensed Matter · Physics 2009-10-22 Jan Brinckmann

A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…

Soft Condensed Matter · Physics 2007-05-23 Prasanth P Jose , Biman Bagchi

We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to…

High Energy Physics - Theory · Physics 2017-11-29 Simone Giombi , Igor R. Klebanov , Grigory Tarnopolsky

We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…

Mathematical Physics · Physics 2025-12-02 Pierluigi Contucci , Claudio Giberti , Godwin Osabutey , Cecilia Vernia

We consider a model of p independent Ising spins on a dynamical planar phi-cubed graph. Truncating the free energy to two terms yields an exactly solvable model that has a third order phase transition from a pure gravity region (gamma=-1/2)…

High Energy Physics - Theory · Physics 2015-06-26 Martin G. Harris

We study large $N$ tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study…

High Energy Physics - Theory · Physics 2017-09-13 Prithvi Narayan , Junggi Yoon

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual…

High Energy Physics - Theory · Physics 2016-12-13 Ronaldo Thibes

Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…

In this article, we illustrate how the qualitative phase diagram of a gauge theory coupled to matter can be directly proved and how rigorous numerical bounds may be established. Our work reaffirms the seminal result of Fradkin and Shenker…

Statistical Mechanics · Physics 2009-11-10 Zohar Nussinov

In this paper we prove, extend and review possible mappings between the two-dimensional Cluster state, Wen's model, the two-dimensional Ising chain and Kitaev's toric code model. We introduce a two-dimensional duality transformation to map…

Quantum Physics · Physics 2014-03-31 Benjamin J. Brown , Wonmin Son , Christina V. Kraus , Rosario Fazio , Vlatko Vedral

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…

High Energy Physics - Theory · Physics 2015-06-26 Shinsuke Nishigaki

We consider a two matrix model with gaussian interaction involving the term $tr ABAB$, which is quartic in angular variables. It describes a vertex model (in particular case - of F-model type) on the lattice of fluctuating geometry and is…

High Energy Physics - Theory · Physics 2016-09-06 Al. Kavalov

We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $\lambda\phi^4$ theory in $d=4-\epsilon$, we obtain the full spectrum of…

High Energy Physics - Theory · Physics 2025-11-12 Oleg Antipin , Jahmall Bersini , Jacob Hafjall , Giulia Muco , Francesco Sannino

We systematically analyze the $d=5$ Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop…

High Energy Physics - Phenomenology · Physics 2015-03-26 D. Aristizabal Sierra , A. Degee , L. Dorame , M. Hirsch

A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…

High Energy Physics - Phenomenology · Physics 2009-11-10 S. Actis , A. Ferroglia , G. Passarino , M. Passera , S. Uccirati