Competition between long-range and short-range interactions in the voter model for opinion dynamics
Year: 2025
Type: article
Abstract: The voter model is a widely used framework in sociophysics to model opinion formation based on local interactions between individuals. In this work, we investigate how the spread of consensus is affected by introducing long-range interactions. Specifically, we study a one-dimensional voter model where a fraction $$\gamma $$ γ of links connect individuals at distances r drawn from a distribution decaying as $$r^{-\sigma -1}$$ r - σ - 1 . Our results reveal that even a small fraction of long-range interactions fundamentally alters the system’s asymptotic behavior. When long-range interactions decay rapidly $$\sigma > 2$$ σ > 2 , their influence is restricted to distances beyond a time-dependent threshold, $$r^*(t)$$ r ∗ ( t ) . For $$r < r^*(t)$$ r < r ∗ ( t ) , the system exhibits short-range dynamics characterized by a Gaussian-like correlation function and a diffusion-driven growth of the correlation length, $$L(t) \sim t^{1/2}$$ L ( t ) ∼ t 1 / 2 . However, for $$r > r^*(t)$$ r > r ∗ ( t ) , the correlation function transitions to a power-law decay, $$r^{-\sigma -1}$$ r - σ - 1 , highlighting the capacity of long-range links to propagate consensus across greater distances. When long-range interactions decay more slowly ( $$\sigma < 2$$ σ < 2 ), they dominate the dynamics at all scales, leading to behavior akin to a system with only long-range interactions. Notably, in the regime $$\sigma < 1$$ σ < 1 long-range links induce a stationary steady state, even for small $$\gamma $$ γ .
Source: The European Physical Journal B
Institution: University of Campania "Luigi Vanvitelli"
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,490
Awards: G490430286, G617794351
OpenAlex ID: W4408736552