On universality of conductivity of planar random self-dual systems

S. A. Bulgadaev

Home/Archive/arXiv

arXiv · cond-mat/0410058

On universality of conductivity of planar random self-dual systems

S. A. Bulgadaev

View original source ↗Read source document ↗Export metadata ↓

Abstract

General properties of the effective conductivity sigma_e of planar isotropic randomly inhomogeneous two-phase self-dual systems are investigated. A new approach for finding out sigma_e of random systems based on a duality, a series expansion in the inhomogeneous parameter z and additional assumptions, is proposed. Two new approximate expressions for sigma_e at arbitrary values of phase concentrations are found. They satisfy all necessary inequalities, symmetries, including a dual one, and reproduce known results in various limiting cases. Two corresponding models with different inhomogeneity structures, whose sigma_e coincide with these expressions, are constructed. First model describes systems with a finite maximal characteristic scale of the inhomogeneities. In this model sigma_e is a solution of the approximate functional equation, generalizing the duality relation. The second model is constructed from squares with random layered structure. The difference of sigma_e for these models means a nonuniversality of the effective conductivity even for binary random self-dual systems. The first explicit expression for sigma_e can be used also for approximate description of various inhomogeneous systems with compact inclusions of the second phase. The percolation problem of these models is briefly discussed.

Explore related subjects

cond-mat.dis-nn cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

S. A. Bulgadaev. 2004-10-03. On universality of conductivity of planar random self-dual systems. https://arxiv.org/abs/cond-mat/0410058

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems

Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2026

Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions

In Euclidean space, universality classes of Anderson transitions are primarily determined by symmetry and spatial dimensionality. Here, we present evidence for a geometry-controlled universality class of non-Hermitian Anderson transitions on hyperbolic-like lattices. In this setting, critical behavior is influenced by the large-scale hyperbolic geometry, characterized by negative curvature, exponential volume growth, and a non-Euclidean notion of spatial scaling. Finite-size scaling of participation ratios across several distinct $ \{p,q\} $ tilings reveals one-parameter scaling collapses with a common critical exponent $ \nu\simeq1 $ within numerical accuracy. A complementary phenomenological coarse-grained Landau-Ginzburg analysis shows how exponential correlation-volume growth suppresses critical fluctuations, offering a rationale for the observed mean-field-like scaling. Our results suggest that spatial curvature can act as an additional organizing principle for Anderson-transition universality beyond the conventional dimensionality- and symmetry-based classification.

cond-mat.dis-nn↗

arXiv2026

Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices

We study finite-rank multiplicative deformations of rotationally invariant non-Hermitian random matrices. More precisely, we consider models of the form $\mathbf{A}(\mathbf{I}+\mathbf{T})$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix, $\mathbf{T}$ is a finite-rank normal perturbation, and $\mathbf{I}$ denotes the identity matrix. We characterize the emergence of outlier eigenvalues, their fluctuations, and the associated eigenvector overlaps. Our results provide a multiplicative non-Hermitian counterpart to the classical Baik--Ben Arous--P\'ech\'e framework.

cond-mat.dis-nn↗