q-neighbor Ising model on a polarized network

• Main Authors: Chmiel, Anna, Sienkiewicz, Julian
• Format: Journal Article
• Language: English
• Published: 30-05-2023
• Subjects: Physics - Disordered Systems and Neural Networks; Physics - Physics and Society; Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2305.19233

In this paper, we examine the interplay between the lobby size $q$ in the
$q$-neighbor Ising model of opinion formation [Phys. Rev. E {\bf 92}, 052105]
and the level of overlap $v$ of two fully connected graphs. Results suggest
that for each lobby size $q \ge 3$, a specific level of overlap $v^*$ exists,
which destroys initially polarized clusters of opinions. By performing
Monte-Carlo simulations, backed by an analytical approach, we show that the
dependence of the $v^*$ on the lobby size $q$ is far from trivial in the
absence of temperature, showing consecutive maximum and minimum, that
additionally depends on the parity of $q$. The temperature is, in general, a
destructive factor; its increase leads to the collapse of polarized clusters
for smaller values of $v$ and additionally brings a substantial decrease in the
level of polarization. However, we show that this behavior is
counter-intuitively inverted for specific lobby sizes and temperature ranges.