We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model [S. Biswas et al., Physica A 391, 3257 (2012)] 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 $p_c\left(q\right)$, 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 ${(p_c\left(q\right)-p)}^{1/2}$ and the relaxation timescale diverges as $|p-p_c{\left(q\right)|}^{-1}$, identical to the original BChS model [S. Biswas et al., Physica A 391, 3257 (2012)]. 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.

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• Critical phenomena
• Noise-induced transitions
• Phase transitions