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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2412.15071 |
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| _version_ | 1866912162028453888 |
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| author | Dumer, R. A. Godoy, M. |
| author_facet | Dumer, R. A. Godoy, M. |
| contents | In this work, we employed the Ising model to identify phase transitions in a magnetic system where the degree distribution of the network follows a power-law and the connections are assortatively mixed. In the Ising model, the spins assume only two values, $σ= \pm 1$, and interact through ferromagnetic coupling $J$. The network is characterized by four variable parameters: $α$ denotes the degree distribution exponent, the minimum degree $k_0$, the maximum degree $k_m$, and the $p_r$ represents the assortativity or disassortativity of the network. To investigate the effect of degree correlations on the critical behavior of the system, we fix $k_0=4$, $k_m=10$, and $α=1$, and vary $p_r$ to obtain an assortative mixing of edges. As result, we have calculated the phase transition points of the system, and the critical exponents related to magnetization $β$, magnetic susceptibility $γ$, and the correlation length $ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase Transitions in a Network with Assortative Mixing Dumer, R. A. Godoy, M. Statistical Mechanics 82M31 I.6.6 In this work, we employed the Ising model to identify phase transitions in a magnetic system where the degree distribution of the network follows a power-law and the connections are assortatively mixed. In the Ising model, the spins assume only two values, $σ= \pm 1$, and interact through ferromagnetic coupling $J$. The network is characterized by four variable parameters: $α$ denotes the degree distribution exponent, the minimum degree $k_0$, the maximum degree $k_m$, and the $p_r$ represents the assortativity or disassortativity of the network. To investigate the effect of degree correlations on the critical behavior of the system, we fix $k_0=4$, $k_m=10$, and $α=1$, and vary $p_r$ to obtain an assortative mixing of edges. As result, we have calculated the phase transition points of the system, and the critical exponents related to magnetization $β$, magnetic susceptibility $γ$, and the correlation length $ν$. |
| title | Phase Transitions in a Network with Assortative Mixing |
| topic | Statistical Mechanics 82M31 I.6.6 |
| url | https://arxiv.org/abs/2412.15071 |