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Related papers: Scaling or multiscaling: Varieties of universality…

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Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…

Statistical Mechanics · Physics 2008-11-26 Malte Henkel , Ulrich Schollwöck

We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…

Statistical Mechanics · Physics 2021-10-19 Pablo Sala , Julius Lehmann , Tibor Rakovszky , Frank Pollmann

Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour…

In this work, we discuss how the linear and non-linear advection terms modify the scaling behavior of the continuous symmetry breaking and stabilize the long-range order, even in $d=2$ far from equilibrium, by means of simple scaling…

Statistical Mechanics · Physics 2024-01-23 Harukuni Ikeda

In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…

Statistical Mechanics · Physics 2009-11-10 Guilhem Semerjian , Leticia F. Cugliandolo , Andrea Montanari

Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…

Physics and Society · Physics 2019-10-16 Marc Barthelemy

Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…

Physics and Society · Physics 2021-01-26 Lei Dong , Zhou Huang , Jiang Zhang , Yu Liu

We present a numerical determination of the scaling functions of the magnetization, the suscep- tibility, and the Binders cumulant, for two nonequilibrium model systems with varying range of interactions. We consider Monte Carlo simulations…

Statistical Mechanics · Physics 2015-06-17 C. I. N. Sampaio-Filho , F. G. B. Moreira

Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality…

Statistical Mechanics · Physics 2009-11-11 T. Hanney , R. B. Stinchcombe

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…

Chaotic Dynamics · Physics 2009-11-11 Luiza Angheluta , Roberto Benzi , Luca Biferale , Itamar Procaccia , Federico Toschi

Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order…

Statistical Mechanics · Physics 2012-06-11 N. V. Antonov , A. V. Malyshev

Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…

Sound · Computer Science 2026-03-17 Victor Zheleznov , Stefan Bilbao , Alec Wright , Simon King

We develop a multiscale approach to describe the behavior of a suspension of solid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. By upscaling the quasi-static Maxwell…

Analysis of PDEs · Mathematics 2020-12-02 Grigor Nika , Bogdan Vernescu

The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…

Data Analysis, Statistics and Probability · Physics 2013-07-01 Shinsuke Koyama

Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…

Statistical Mechanics · Physics 2008-11-26 N. V. Antonov , A. A. Ignatieva

The existence of unique scaling in a crossover regime between viscous and inertial hydrodynamic regimes is revealed for homogeneous, isotropic, incompressible, spinodal turbulence which is characterized, to begin with, by three different…

Soft Condensed Matter · Physics 2007-05-23 R. V. R. Pandya

The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of…

Statistical Mechanics · Physics 2018-03-01 Lucas Böttcher , Hans Jürgen Herrmann , Malte Henkel

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

Numerical Analysis · Mathematics 2021-08-10 Fabrizio Greco , Lorenzo Leonetti , Paolo Lonetti , Raimondo Luciano , Andrea Pranno

The critical behavior of driven lattice gas models has been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in the universality classes…

Statistical Mechanics · Physics 2019-09-04 Yahui Li , Zhongda Zeng , Fan Zhong

After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…

Mathematical Physics · Physics 2021-11-01 Alessandro Giuliani