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

arXiv:cond-mat/0403471 · Physical Review E

Violation of the Widom scaling law for effective crossover exponents

S. Lübeck

Published Jun 1, 2004• 7 citations
arXivHTMLPDF

Abstract

In this work we consider the universal crossover behavior of two nonequilibrium systems exhibiting a continuous phase transition. Focusing on the field driven crossover from mean-field to non-mean-field scaling behavior we show that the well-known Widom scaling law is violated for the effective exponents in the so-called crossover regime.

DOI
10.1103/physreve.69.066101

Related papers

Universal Behavior of Crossover Scaling Functions for Continuous Phase Transitions

S. Lübeck

We consider two different systems exhibiting a continuous phase transition into an absorbing state. Both models belong to the same universality class; i.e., they are characterized by the same scaling functions and the same critical exponents. Varying the range of interactions, we examine the crossover from the mean-field-like to the non-mean-field scaling behavior. A phenomenological scaling form is applied in order to describe the full crossover region, which spans several decades. Our results strongly support the hypothesis that the crossover function is universal.

arXiv:cond-mat/0307316•Physical Review Letters•May 27, 2003•15 citations

Fixed Points and Crossovers for the Hysteresis Scaling of Dynamic Mean-Field Models

Jie Yang, Fan Zhong

Abstract Phase transitions are divided into first-order and continuous ones in the current classification. While the latter shows striking phenomena of scaling and universality, the former is typically characterized by discontinuous jumps in extensive variables and pronounced hysteresis. Recent studies have demonstrated universal scaling behavior controlled by a cubic fixed point in first-order phase transitions. However, more recent investigations of hysteresis in a dynamic mean-field quartic model driven across its first-order phase transitions have revealed new scaling exponents for different driving rates. Here, we discover a new exponent for large driving rates arising surprisingly from critical phenomena and show that, depending on the magnitude of the driving rates and the absence or presence of noise, the same mean-field model remarkably exhibits several universality classes with definite universal scaling exponents governed by their corresponding fixed points, as revealed through a systematic scaling analysis based on renormalization group theory. The theories, the various crossovers between different fixed points, and the complete universal scaling of full curve collapse, are all verified by numerical results. This further confirms universal scaling in first-order phase transitions.

arXiv:2605.00567•Chinese Physics Letters•Jun 23, 2026•1 citation

Universal Scaling Behavior at the Upper Critical Dimension of Nonequilibrium Continuous Phase Transitions

S. Lübeck, P. C. Heger

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a nonequilibrium continuous phase transition. By focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and nonequilibrium phase transitions observed numerically or experimentally.

arXiv:cond-mat/0307353•Physical Review Letters•Jun 12, 2003•43 citations

Scaling in Spin-Glasses

Daniel S. Fisher, Haim Sompolinsky

Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at $d=6$ scaling is restored. Below $d=6$ all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.

Physical Review Letters•Mar 11, 1985•82 citations

Universal finite-size scaling behavior and universal dynamical scaling behavior of absorbing phase transitions with a conserved field

S. Lübeck, P. C. Heger

We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows one to validate certain hyperscaling relations. Using these hyperscaling relations it is possible to express the avalanche exponents of a self-organized critical system in terms of the ordinary exponents of a continuous absorbing phase transition.

arXiv:cond-mat/0309165•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 3, 2003•105 citations

Finite-size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation

Richard L. C. Vink, Timo Fischer, Kurt Binder

In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.

arXiv:1008.3299•Physical Review E•Nov 30, 2010•44 citations
In this work we consider the universal crossover behavior of two nonequilibrium systems exhibiting a continuous phase transition. Focusing on the field driven crossover from mean-field to non-mean-field scaling behavior we show that the well-known Widom scaling law is violated for the effective exponents in the so-called crossover regime.
We consider two different systems exhibiting a continuous phase transition into an absorbing state. Both models belong to the same universality class; i.e., they are characterized by the same scaling functions and the same critical exponents. Varying the range of interactions, we examine the crossover from the mean-field-like to the non-mean-field scaling behavior. A phenomenological scaling form is applied in order to describe the full crossover region, which spans several decades. Our results strongly support the hypothesis that the crossover function is universal.
Abstract Phase transitions are divided into first-order and continuous ones in the current classification. While the latter shows striking phenomena of scaling and universality, the former is typically characterized by discontinuous jumps in extensive variables and pronounced hysteresis. Recent studies have demonstrated universal scaling behavior controlled by a cubic fixed point in first-order phase transitions. However, more recent investigations of hysteresis in a dynamic mean-field quartic model driven across its first-order phase transitions have revealed new scaling exponents for different driving rates. Here, we discover a new exponent for large driving rates arising surprisingly from critical phenomena and show that, depending on the magnitude of the driving rates and the absence or presence of noise, the same mean-field model remarkably exhibits several universality classes with definite universal scaling exponents governed by their corresponding fixed points, as revealed through a systematic scaling analysis based on renormalization group theory. The theories, the various crossovers between different fixed points, and the complete universal scaling of full curve collapse, are all verified by numerical results. This further confirms universal scaling in first-order phase transitions.
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a nonequilibrium continuous phase transition. By focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and nonequilibrium phase transitions observed numerically or experimentally.
Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at d=6d=6d=6 scaling is restored. Below d=6d=6d=6 all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.