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Related papers: Large N limit of O(N) vector models

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The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, often called the \emph{Sinkhorn limit} of $A$. The main result in this paper…

Rings and Algebras · Mathematics 2019-10-01 Melvyn B. Nathanson

We consider the Derivative NLS equation with general quadratic nonlinearities. In \cite{be2} the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension $n =…

Analysis of PDEs · Mathematics 2007-05-23 Ioan Bejenaru , Daniel Tataru

A family of models for fluctuating loops in a two dimensional random background is analyzed. The models are formulated as O(n) spin models with quenched inhomogeneous interactions. Using the replica method, the models are mapped to the…

Disordered Systems and Neural Networks · Physics 2009-08-03 Hirohiko Shimada

In this work, we investigate the effects of logarithms on the asymptotic behavior of power expansion/OPE in supper-renormalizable QFTs. We performed a careful investigation of the large $p^2$ expansion of a scalar-scalar two-point function…

High Energy Physics - Theory · Physics 2025-08-06 Yizhuang Liu

In this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2<D<4 and 4<D<6. Based on a…

High Energy Physics - Theory · Physics 2022-03-09 Rafael Moser , Domenico Orlando , Susanne Reffert

Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for…

High Energy Physics - Lattice · Physics 2008-11-26 K. Kajantie , M. Laine , T. Neuhaus , A. Rajantie , K. Rummukainen

We explore the deep ultraviolet (that is, short-distance) limit of the power spectrum (PS) and of the correlation function of a cold dark matter dominated Universe. While for large scales the PS can be written as a double series expansion,…

Cosmology and Nongalactic Astrophysics · Physics 2020-07-01 Shi-Fan Chen , Massimo Pietroni

We determine some points on the finite size scaling curve for the correlation length in the two dimensional O(3) and icosahedron spin models. The Monte Carlo data are consistent with the two models possessing the same continuum limit. The…

High Energy Physics - Lattice · Physics 2009-11-07 Adrian Patrascioiu , Erhard Seiler

An extended superscaling analysis of quasielastic electron scattering data is proposed by parametrizing the scaling function as the sum of a symmetric function corresponding to the emission of a single particle plus a contribution from the…

Nuclear Theory · Physics 2024-03-05 V. L. Martinez-Consentino , J. E. Amaro , P. R. Casale , I. Ruiz Simo

The Kontsevich-Penner model, an Airy matrix model with a logarithmic potential, may be derived from a simple Gaussian two-matrix model through a duality. In this dual version the Fourier transforms of the n-point correlation functions can…

Mathematical Physics · Physics 2015-05-30 E. Brezin , S. Hikami

I review some recent work on the problem of multiparticle production in a phi^4-theory with an O(N) symmetry. Threshold amplitudes with fixed number of produced particles are exactly calculated at large-N to all loops and vanish on mass…

High Energy Physics - Phenomenology · Physics 2007-05-23 Yu. Makeenko

Strong-coupling analysis of two-dimensional chiral models, extended to 15th order, allows for the identification of a scaling region where known continuum results are reproduced with great accuracy, and asymptotic scaling predictions are…

High Energy Physics - Lattice · Physics 2009-12-30 Massimo Campostrini , Paolo Rossi , Ettore Vicari

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…

High Energy Physics - Theory · Physics 2009-11-07 Emil T. Akhmedov , Philip DeBoer , Gordon W. Semenoff

In recent years, energy correlators have emerged as a powerful tool to explore the field theoretic structure of strong interactions at particle colliders. In this Letter we initiate a novel study of the non-perturbative power corrections to…

High Energy Physics - Phenomenology · Physics 2025-01-07 Hao Chen , Pier Francesco Monni , Zhen Xu , Hua Xing Zhu

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case…

High Energy Physics - Phenomenology · Physics 2016-04-19 Gergely Markó , Urko Reinosa , Zsolt Szép

In this note we study two point functions of Coulomb branch chiral ring elements with large $R$-charge, in quantum field theories with ${\mathcal N} = 2$ superconformal symmetry in four spacetime dimensions. Focusing on the case of…

High Energy Physics - Theory · Physics 2018-01-03 Simeon Hellerman , Shunsuke Maeda

Many machine learning models based on neural networks exhibit scaling laws: their performance scales as power laws with respect to the sizes of the model and training data set. We use large-N field theory methods to solve a model recently…

High Energy Physics - Theory · Physics 2024-05-31 Zhengkang Zhang

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Machine Learning · Computer Science 2022-11-01 Alexander Maloney , Daniel A. Roberts , James Sully

We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in $0+1$ dimensions, with $D$ matrices, and use $1/D$ as an expansion parameter. This can be thought of as a non-commutative…

High Energy Physics - Theory · Physics 2024-12-03 Takanori Anegawa , Norihiro Iizuka , Daniel Kabat

The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using the exact renormalization group equations has been studied, motivated by the recently found non-trivial fixed point in $4<d<6$ dimensions with metastable critical…

High Energy Physics - Theory · Physics 2016-09-28 P. Mati