Geometrical interpretation of critical exponents

被引：0

作者：

Lima, Henrique A. ^{[1
]}

Luis, Edwin E. Mozo ^{[2
]}

Carrasco, Ismael S. S. ^{[1
]}

Hansen, Alex ^{[3
]}

Oliveira, Fernando A. ^{[1
,2
]}

机构：

[1] Univ Brasilia, Inst Phys, Int Ctr Phys, BR-70910900 Brasilia, DF, Brazil

[2] Univ Fed Fluminense, Inst Fis, Ave Litoranea S-N, BR-24210340 Niteroi, RJ, Brazil

[3] Norwegian Univ Sci & Technol, Dept Phys, PoreLab, NO-7491 Trondheim, Norway

来源：

PHYSICAL REVIEW E | 2024年 / 110卷 / 06期

关键词：

FLUCTUATION-DISSIPATION-THEOREM; VIOLATION; CLUSTERS; DYNAMICS;

D O I：

10.1103/PhysRevE.110.L062107

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We develop a hypothesis that the dynamics of equilibrium systems at criticality have their dynamics constricted to a fractal subspace. We relate the correlation fractal dimension associated with this subspace to the Fisher critical exponent controlling the singularity associated with the correlation function. This fractal subspace is different from that associated with the order parameter. We propose a relation between the correlation fractal dimension and the order parameter fractal dimension. The fractal subspace we identify has as a defining property that the correlation function is restored at the critical point by restricting the dynamics this way. We determine the correlation fractal dimension of the two-dimensional Ising model and validate it by computer simulations. We discuss growth models briefly in this context.

引用

页数：5

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