Interplay of choice and topology in percolation on mediation-driven attachment networks
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arXiv
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| Format: | Preprint |
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2025
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| author | Roy, Nilomber Sheraj, M. M. B. Hassan, M. K. |
| author_facet | Roy, Nilomber Sheraj, M. M. B. Hassan, M. K. |
| contents | We investigate bond percolation on mediation-driven attachment (MDA) networks under the generalized Achlioptas process, where $M>1$ candidate bonds are sampled and the one that minimizes the resulting cluster size is selected the best-of-$M$ rule. This framework offers a systematic approach to investigate how network topology and choice mechanisms jointly shape percolation behavior. We analyze the effects of the degree exponent $ω$ and the choice parameter $M$ on the critical point $t_c$ and the critical exponents ($β,α,γ$), which define universality classes and obey the Rushbrooke inequality $α+ 2β+ γ\geq 2$. Using entropy, the order parameter, and their derivatives (representing specific heat and susceptibility respectively), we show that both $t_c$ and the universality class depend only weakly on $ω$ but strongly on $M$, while the Rushbrooke inequality remains valid throughout. For $M=2$, the order parameter varies continuously without a clear order-disorder transition. By contrast, $M=3$ and $M=4$ display explosive percolation that still corresponds to a continuous phase transition, with $M=4$ producing a significantly sharper and clearer order-disorder transition. This sharpening is traced to an enhanced powder-keg effect at larger $M$, underscoring the entropic origin of explosive percolation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interplay of choice and topology in percolation on mediation-driven attachment networks Roy, Nilomber Sheraj, M. M. B. Hassan, M. K. Statistical Mechanics Physics and Society We investigate bond percolation on mediation-driven attachment (MDA) networks under the generalized Achlioptas process, where $M>1$ candidate bonds are sampled and the one that minimizes the resulting cluster size is selected the best-of-$M$ rule. This framework offers a systematic approach to investigate how network topology and choice mechanisms jointly shape percolation behavior. We analyze the effects of the degree exponent $ω$ and the choice parameter $M$ on the critical point $t_c$ and the critical exponents ($β,α,γ$), which define universality classes and obey the Rushbrooke inequality $α+ 2β+ γ\geq 2$. Using entropy, the order parameter, and their derivatives (representing specific heat and susceptibility respectively), we show that both $t_c$ and the universality class depend only weakly on $ω$ but strongly on $M$, while the Rushbrooke inequality remains valid throughout. For $M=2$, the order parameter varies continuously without a clear order-disorder transition. By contrast, $M=3$ and $M=4$ display explosive percolation that still corresponds to a continuous phase transition, with $M=4$ producing a significantly sharper and clearer order-disorder transition. This sharpening is traced to an enhanced powder-keg effect at larger $M$, underscoring the entropic origin of explosive percolation. |
| title | Interplay of choice and topology in percolation on mediation-driven attachment networks |
| topic | Statistical Mechanics Physics and Society |
| url | https://arxiv.org/abs/2510.10076 |