Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Generic features of fluctuations in critical systems

B. Zheng

Published Feb 14, 2003• 24 citations
Publisher

Abstract

The probability distribution function of magnetization of critical magnetic systems is investigated with Monte Carlo simulations. Its generic features beyond the standard universality are revealed. A mean field ansatz explains the phenomena partly.
DOI
10.1103/physreve.67.026114

Related papers

Universalidad generalizada en sistemas de tamaño finito altamente correlacionados

Guillermo Palma, T. I. Meyer, Raúl Labbé

In recents works [1] (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. This universal behavior was attributed to systems sharing the the properties of high correlations, self-organized criticality and finite size effects. To study these phenomena, we performed a high precision Monte Carlo (MC) simulation of the 2DXY-model [2]. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size, below the Kosterlitz-Thoules temperature [3]. However, the shape of these distributions do depend on the temperature, contrarily to the claim of (BHP). This behaviour is succesfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.

Revista Mexicana de Física•Nov 1, 2002•0 citations

Generalization of the central limit theorem to critical systems: Revisiting perturbation theory

Sankarshan Sahu, Bertrand Delamotte, Adam Rançon

The central limit theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode has been performed with the functional renormalization group in the case of the three-dimensional Ising model [Balog et al., Phys. Rev. Lett. 129, 210602 (2022)10.1103/PhysRevLett.129.210602]. It has been shown in that article that there exists an entire family of universal PDFs parameterized by ζ=lim_{L,ξ_{∞}→∞}L/ξ_{∞} which is the ratio of the system size L to the bulk correlation length ξ_{∞} with both the thermodynamic limit and the critical limit being taken simultaneously. We show how these PDFs or, equivalently, the rate functions which are their logarithm, can be systematically computed perturbatively in the ε=4-d expansion. We determine the whole family of universal PDFs and show that they are in good qualitative agreement with Monte Carlo data. Finally, we conjecture on how to significantly improve the quantitative agreement between the one-loop and the numerical results.

arXiv:2407.12603•Physical review. E•Mar 26, 2025•6 citations

Critical slowing down in local dynamics simulations

Hans-O Heuer

The author reports some universal and non-universal aspects of the critical dynamics of the three-dimensional Ising model, obtained in extensive Monte Carlo finite-size simulations. The author shows that the time-dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point: (i) phase fluctuations from one metastable minimum of the free energy to the other, dominating the long-time behaviour of the magnetization; (ii) critical fluctuations inside each minimum, decaying on a comparatively short timescale. Both kinds of fluctuations show up the same critical exponent z=2.10+or-0.02, which is also in excellent agreement with the exponent z of energy fluctuations.

Journal of Physics A Mathematical and General•May 7, 1992•25 citations

Criticality in diluted ferromagnets

Elena Agliari, Adriano Barra A, Federico Camboni

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet using analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non-trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results.

arXiv:0804.4503•Journal of Statistical Mechanics Theory and Experiment•Oct 7, 2008•32 citations

Spontaneous magnetization probability distribution of a mean-field finite Ising model exhibiting a tricritical point

Santiago Velasco, Juan A. White, J. Güémez

Physica A Statistical Mechanics and its Applications•May 1, 1996•0 citations

Universal features of fluctuations

Robert S. Botet, Marek Płoszajczak

Universal scaling laws of fluctuations (the $\\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can be identified, the relation between order parameter, criticality and scaling law of fluctuations has been established and the relation between the scaling function and the critical exponents has been found.

•Jan 1, 2001•5 citations
In recents works [1] (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. This universal behavior was attributed to systems sharing the the properties of high correlations, self-organized criticality and finite size effects. To study these phenomena, we performed a high precision Monte Carlo (MC) simulation of the 2DXY-model [2]. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size, below the Kosterlitz-Thoules temperature [3]. However, the shape of these distributions do depend on the temperature, contrarily to the claim of (BHP). This behaviour is succesfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.
The central limit theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode has been performed with the functional renormalization group in the case of the three-dimensional Ising model [Balog et al., Phys. Rev. Lett. 129, 210602 (2022)10.1103/PhysRevLett.129.210602]. It has been shown in that article that there exists an entire family of universal PDFs parameterized by ζ=lim_{L,ξ_{∞}→∞}L/ξ_{∞} which is the ratio of the system size L to the bulk correlation length ξ_{∞} with both the thermodynamic limit and the critical limit being taken simultaneously. We show how these PDFs or, equivalently, the rate functions which are their logarithm, can be systematically computed perturbatively in the ε=4-d expansion. We determine the whole family of universal PDFs and show that they are in good qualitative agreement with Monte Carlo data. Finally, we conjecture on how to significantly improve the quantitative agreement between the one-loop and the numerical results.
The author reports some universal and non-universal aspects of the critical dynamics of the three-dimensional Ising model, obtained in extensive Monte Carlo finite-size simulations. The author shows that the time-dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point: (i) phase fluctuations from one metastable minimum of the free energy to the other, dominating the long-time behaviour of the magnetization; (ii) critical fluctuations inside each minimum, decaying on a comparatively short timescale. Both kinds of fluctuations show up the same critical exponent z=2.10+or-0.02, which is also in excellent agreement with the exponent z of energy fluctuations.
We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet using analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non-trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results.
Universal scaling laws of fluctuations (the Delta\\DeltaDelta-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can be identified, the relation between order parameter, criticality and scaling law of fluctuations has been established and the relation between the scaling function and the critical exponents has been found.