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Related papers: Hierarchical Spherical Model from a Geometric Poin…

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Generalizing methods developed by Pinn, Pordt and Wieczerkowski for the hierarchical model with one component (N=1) and dimensions d between 2 and 4 we compute O(N)-symmetric fixed points of the hierarchical renormalization group equation…

Statistical Mechanics · Physics 2007-05-23 J. Goettker-Schnetmann

We investigate the GOY shell model within the scenario of a critical dimension in fully developed turbulence. By changing the conserved quantities, one can continuously vary an ``effective dimension'' between $d=2$ and $d=3$. We identify a…

Chaotic Dynamics · Physics 2009-11-07 Paolo Giuliani , Mogens H. Jensen , Victor Yakhot

We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the…

Disordered Systems and Neural Networks · Physics 2019-07-16 Yoshinori Sakamoto

We revisit the relation between the spherical model of Berlin-Kac and the spin $O(N)$ model in the limit $N \to \infty$, and explain how they are connected via the discrete Gaussian free field (GFF). Using probabilistic limit theorems and…

Probability · Mathematics 2025-09-04 Juhan Aru , Aleksandra Korzhenkova

The 2D RP(2) gauge model is studied using the Monte-Carlo Renormalization Group. We confirm the first-order transition reported by Solomon et al. (PL 112B, (1982)) ending in a critical point associated with vorticity. We find evidence for a…

High Energy Physics - Lattice · Physics 2009-10-30 S. M. Caterall , M. Hasenbusch , R. R. Horgan , R. L. Renken

The critical dynamics of Model H with a conserved order parameter coupled to a transverse momentum density which describes the gas-liquid or binary-fluid transitions is investigated within the functional renormalization group approach…

High Energy Physics - Phenomenology · Physics 2024-10-08 Yong-rui Chen , Yang-yang Tan , Wei-jie Fu

We consider dimensional crossover for an O(N) model on a d-dimensional layered geometry of thickness L, in the sigma-model limit, using ``environmentally friendly'' renormalization. We show how to derive critical temperature shifts, giving…

Statistical Mechanics · Physics 2007-05-23 Denjoe O'Connor , C. R. Stephens , J. A. Santiago

We consider a model of discretized 2d gravity interacting with Ising spins where phase boundaries are restricted to have minimal length and show analytically that the critical exponent $\gamma= 1/3$ at the spin transition point. The model…

High Energy Physics - Theory · Physics 2015-06-26 J. Ambjorn , B. Durhuus , T. Jonsson

In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these…

High Energy Physics - Lattice · Physics 2009-10-28 Massimo Campostrini , Attilio Cucchieri , Tereza Mendes , Andrea Pelissetto , Paolo Rossi , Alan D. Sokal , Ettore Vicari

We reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…

High Energy Physics - Theory · Physics 2016-04-19 Kazuhiko Kamikado , Takuya Kanazawa

By using renormalization-group (RG) methods, we study a non-mean-field model of a spin glass built on a hierarchical lattice, the hierarchical Edwards-Anderson model in a magnetic field. We investigate the spin-glass transition in a field…

Disordered Systems and Neural Networks · Physics 2015-03-03 Michele Castellana , Carlo Barbieri

The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping…

Statistical Mechanics · Physics 2009-11-10 P. Calabrese , P. Parruccini , A. I. Sokolov

We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical…

Probability · Mathematics 2019-10-31 Paolo Dai Pra , Marco Formentin , Guglielmo Pelino

We use our recently developed functional renormalization group (FRG) approach for quantum spin systems to investigate the phase diagram of the frustrated $J_{1}J_{2}J_{3}$ quantum Heisenberg model on a cubic lattice. From a simple…

Strongly Correlated Electrons · Physics 2023-02-28 Dmytro Tarasevych , Andreas Rückriegel , Savio Keupert , Vasilios Mitsiioannou , Peter Kopietz

We present real--space renormalization group (RG) calculations of the critical properties of the random--field Ising model on a cubic lattice in three dimensions. We calculate the RG flows in a two--parameter truncation of the Hamiltonian…

Condensed Matter · Physics 2009-10-22 M. E. J. Newman , B. W. Roberts , G. T. Barkema , J. P. Sethna

We investigate the XY spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to L=12 (2D) and L=8 (3D) strongly suggest that the lower critical dimension…

Disordered Systems and Neural Networks · Physics 2009-10-30 J. Maucourt , D. R. Grempel

We focus on two real-space renormalization-group (RG) methods recently proposed for a hierarchical model of a spin glass: A sample-by-sample method, in which the RG transformation is performed separately on each disorder sample, and an…

Disordered Systems and Neural Networks · Physics 2019-10-11 Michele Castellana

In this article we report a preliminary investigation of the large $N$ limit of a generalized one-matrix model which represents an $O(n)$ symmetric model on a random lattice. The model on a regular lattice is known to be critical only for…

High Energy Physics - Theory · Physics 2009-10-22 B. Eynard , J. Zinn-Justin

The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general…

Condensed Matter · Physics 2009-10-30 Hassan Chamati , Ekaterina S. Pisanova , Nocholay S. Tonchev

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in $3 \leq d\leq 6$ Euclidean…

High Energy Physics - Theory · Physics 2016-07-12 Xin An , David Mesterházy , Mikhail A. Stephanov