Generalized BChS Model with Group Interactions: Shift in the Critical Point and Mean-Field Ising Universality
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910128371924992 |
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| author | Pradhan, Amit |
| author_facet | Pradhan, Amit |
| contents | We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model \cite{Biswas} with group interactions of size $q$, extending the original pairwise interaction dynamics. Within a mean-field framework, we derive an exact expression for the critical noise $p_c(q)$, showing that it increases monotonically with $q$ and approaches $1/2$ in the large-$q$ limit, consistent with a Gaussian approximation. Despite this shift in the phase boundary, the critical behavior remains unchanged across all $q$: the order parameter scales as $(p_c(q)-p)^{1/2}$, and the relaxation timescale diverges as $|p-p_c(q)|^{-1}$, identical to the original BChS model \cite{Biswas}. Finite-size scaling of the Binder cumulant, order parameter, and its fluctuations confirm that the system belongs to the mean-field Ising universality class for all $q$. Our results demonstrate that higher-order interactions modify the location of the transition without altering its universality class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12430 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized BChS Model with Group Interactions: Shift in the Critical Point and Mean-Field Ising Universality Pradhan, Amit Statistical Mechanics We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model \cite{Biswas} with group interactions of size $q$, extending the original pairwise interaction dynamics. Within a mean-field framework, we derive an exact expression for the critical noise $p_c(q)$, showing that it increases monotonically with $q$ and approaches $1/2$ in the large-$q$ limit, consistent with a Gaussian approximation. Despite this shift in the phase boundary, the critical behavior remains unchanged across all $q$: the order parameter scales as $(p_c(q)-p)^{1/2}$, and the relaxation timescale diverges as $|p-p_c(q)|^{-1}$, identical to the original BChS model \cite{Biswas}. Finite-size scaling of the Binder cumulant, order parameter, and its fluctuations confirm that the system belongs to the mean-field Ising universality class for all $q$. Our results demonstrate that higher-order interactions modify the location of the transition without altering its universality class. |
| title | Generalized BChS Model with Group Interactions: Shift in the Critical Point and Mean-Field Ising Universality |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.12430 |