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/9603129 · International Journal of Modern Physics A

FLOW OF THE COARSE GRAINED FREE ENERGY FOR CROSSOVER PHENOMENA

S. BORNHOLDT, P. BÜTTNER, N. Tetradis, C. WETTERICH

Published Mar 10, 1999• 4 citations
arXivHTMLPDF

Abstract

The critical behavior of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behavior, the flow of the coarse grained free energy also describes the approach to scaling.

DOI
10.1142/s0217751x99000440

Related papers

Flow of the Coarse Grained Free Energy for Crossover Phenomena

Stefan Bornholdt, Buettner, P. (Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik), N. Tetradis +2 more

The critical behaviour of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behaviour, the flow of the coarse grained free energy also describes the approach to scaling. (orig.)

•Jan 1, 1996•4 citations

Critical Equation of State from the Average Action

Jürgen Berges, N. Tetradis, CHRISTOF WETTERICH

The scaling form of the critical equation of state is computed for $O(N)$-symmetric models. We employ a method based on an exact flow equation for a coarse-grained free energy. A suitable truncation is solved numerically.

arXiv:hep-th/9507159•Physical Review Letters•Jul 29, 1996•78 citations

Effective average action in statistical physics and quantum field theory

Wetterich, C

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.

•Jan 16, 2001•58 citations

Effective critical and tricritical exponents

Eberhard K. Riedel, Franz Wegner

A semi-microscopic scaling-field theory is developed for crossover phenomena near critical and tricritical points. The theory is based on a renormalization-group description of a model with two competing fixed points (such as a critical and a tricritical fixed point) in terms of scaling fields. The coupled nonlinear differential equations for scaling fields are truncated such as to preserve the physics essential for crossover phenomena. The approach allows the explicit calculation of thermodynamic functions for (i) tricritical systems and (ii) critical systems with an irrelevant scaling field. We obtain, for example, an explicit expression for the scaling function of the susceptibility, which describes the crossover from the tricritical to the critical region. The idea of "flow diagrams" in the scaling-field space is used to characterize crossover phenomena globally in the whole critical region. The concept of asymptotic critical exponents is generalized and effective critical exponents are introduced as logarithmic derivatives of thermodynamic quantities with respect to experimental fields and scaling fields, respectively. By using the method of effective exponents the size of the crossover region between regions of different asymptotic critical behavior is estimated. For the susceptibility, the width of the crossover region in decades of the effective temperature variable is roughly equal to the inverse of the crossover exponent. In the case of a critical system with a slow transient the asymptotic critical exponent is only reached extremely close to the critical point (unless the amplitude of the transient vanishes). It might then be impossible to determine the asymptotic exponent experimentally or by conventional series-expansion techniques, and an analysis of the data in terms of effective exponents is the alternative. The scaling-field approach is applied to three systems with crossover phenomena: (i) the model for tricritical systems with molecular-field tricritical exponents, (ii) the Ashkin-Teller model in three dimensions, and (iii) a model for phase transitions with Fisher exponent renormalization due to a constraint.

Physical review. B, Solid state•Jan 1, 1974•194 citations

Time coarse graining near critical points

Ann Bruce, David B. Nicolaides

The authors investigate the statistical properties of local variables, coarse grained in time, in systems undergoing continuous phase transitions. A general theory is developed which suggests universal scaling behaviour in the limit of large coarse-graining times. The predictions are substantiated with Monte Carlo studies of two-dimensional scalar models. A simple fractal model of the time profile of the ordering variable is developed which captures and illuminates its timescale-invariant character. The theory is used to study the critical behaviour of local resonance lineshapes. In the two-dimensional case studied explicitly the critical slowing down is shown to drive a crossover to a split slow-motion lineshape.

Journal of Physics A Mathematical and General•Dec 21, 1987•0 citations

EFFECTIVE AVERAGE ACTION IN STATISTICAL PHYSICS AND QUANTUM FIELD THEORY

CHRISTOF WETTERICH

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.

arXiv:hep-ph/0101178•International Journal of Modern Physics A•Apr 30, 2001•90 citations
The critical behavior of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behavior, the flow of the coarse grained free energy also describes the approach to scaling.
The scaling form of the critical equation of state is computed for O(N)O(N)O(N)-symmetric models. We employ a method based on an exact flow equation for a coarse-grained free energy. A suitable truncation is solved numerically.
A semi-microscopic scaling-field theory is developed for crossover phenomena near critical and tricritical points. The theory is based on a renormalization-group description of a model with two competing fixed points (such as a critical and a tricritical fixed point) in terms of scaling fields. The coupled nonlinear differential equations for scaling fields are truncated such as to preserve the physics essential for crossover phenomena. The approach allows the explicit calculation of thermodynamic functions for (i) tricritical systems and (ii) critical systems with an irrelevant scaling field. We obtain, for example, an explicit expression for the scaling function of the susceptibility, which describes the crossover from the tricritical to the critical region. The idea of "flow diagrams" in the scaling-field space is used to characterize crossover phenomena globally in the whole critical region. The concept of asymptotic critical exponents is generalized and effective critical exponents are introduced as logarithmic derivatives of thermodynamic quantities with respect to experimental fields and scaling fields, respectively. By using the method of effective exponents the size of the crossover region between regions of different asymptotic critical behavior is estimated. For the susceptibility, the width of the crossover region in decades of the effective temperature variable is roughly equal to the inverse of the crossover exponent. In the case of a critical system with a slow transient the asymptotic critical exponent is only reached extremely close to the critical point (unless the amplitude of the transient vanishes). It might then be impossible to determine the asymptotic exponent experimentally or by conventional series-expansion techniques, and an analysis of the data in terms of effective exponents is the alternative. The scaling-field approach is applied to three systems with crossover phenomena: (i) the model for tricritical systems with molecular-field tricritical exponents, (ii) the Ashkin-Teller model in three dimensions, and (iii) a model for phase transitions with Fisher exponent renormalization due to a constraint.
The authors investigate the statistical properties of local variables, coarse grained in time, in systems undergoing continuous phase transitions. A general theory is developed which suggests universal scaling behaviour in the limit of large coarse-graining times. The predictions are substantiated with Monte Carlo studies of two-dimensional scalar models. A simple fractal model of the time profile of the ordering variable is developed which captures and illuminates its timescale-invariant character. The theory is used to study the critical behaviour of local resonance lineshapes. In the two-dimensional case studied explicitly the critical slowing down is shown to drive a crossover to a split slow-motion lineshape.