q-neighbor Ising model on a polarized network
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arXiv
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| Natura: | Preprint |
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2023
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| _version_ | 1866912150925082624 |
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| author | Chmiel, Anna Sienkiewicz, Julian |
| author_facet | Chmiel, Anna Sienkiewicz, Julian |
| contents | In this paper, we examine the interplay between the lobby size $q$ in the $q$-neighbor Ising model of opinion formation (Phys. Rev. E 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19233 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | q-neighbor Ising model on a polarized network Chmiel, Anna Sienkiewicz, Julian Statistical Mechanics Disordered Systems and Neural Networks Physics and Society In this paper, we examine the interplay between the lobby size $q$ in the $q$-neighbor Ising model of opinion formation (Phys. Rev. E 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. |
| title | q-neighbor Ising model on a polarized network |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Physics and Society |
| url | https://arxiv.org/abs/2305.19233 |