Generalized Biswas-Chatterjee-Sen model with group interactions: Shift in the critical point and mean-field Ising universality.

We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model [S. Biswas et al., Physica A 391, 3257 (2012)0378-437110.1016/j.physa.2012.01.046] 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 [S. Biswas et al., Physica A 391, 3257 (2012)0378-437110.1016/j.physa.2012.01.046]. 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.