Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1510.04467

From Microscopic Heterogeneity to Macroscopic Complexity in the Contrarian Voter Model

Sven Banisch
View original source ↗Read source document ↗Export metadata ↓

Abstract

An analytical treatment of a simple opinion model with contrarian behavior is presented. The focus is on the stationary dynamics of the model and in particular on the effect of inhomogeneities in the interaction topology on the stationary behavior. We start from a micro-level Markov chain description of the model. Markov chain aggregation is then used to derive a macro chain for the complete graph as well as a meso-level description for the two-community graph composed of two (weakly) coupled sub-communities. In both cases, a detailed understanding of the model behavior is possible using Markov chain tools. More importantly, however, this setting provides an analytical scenario to study the discrepancy between the homogeneous mixing case and the model on a slightly more complex topology. We show that memory effects are introduced at the macro level when we aggregate over agent attributes without sensitivity to the microscopic details and quantify these effects using concepts from information theory. In this way, the method facilitates the analysis of the relation between microscopic processes and a their aggregation to a macroscopic level of description and informs about the complexity of a system introduced by heterogeneous interaction relations.

Explore related subjects

cond-mat.stat-mechcs.ITmath.ITnlin.AOphysics.data-an

Keep this discovery

BibTeXRIS

Sven Banisch. 2015-10-15. From Microscopic Heterogeneity to Macroscopic Complexity in the Contrarian Voter Model. https://doi.org/10.1142/s0219525914500258

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

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗
arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗
arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗