https://doi.org/10.1140/epjb/s10051-025-00928-z
Regular Article - Statistical and Nonlinear Physics
Is directed percolation class for synchronization transition robust with multi-site interactions?
1
Department of CSE, GH Raisoni Skill Tech University, Nagpur, India
2
Department of Physics, RTM Nagpur University, Nagpur, India
Received:
16
October
2024
Accepted:
15
April
2025
Published online:
25
April
2025
Coupled map lattice with pairwise local interactions is a well-studied system. However, in several situations, such as neuronal or social networks, multi-site interactions are possible. In this work, we study the coupled Gauss map in one dimension with 2-site, 3-site, 4-site and 5-site interaction. This coupling cannot be decomposed in pairwise interactions. We coarse-grain the variable values by labeling the sites above 
as up spin (+ 1) and the rest as down spin (– 1) where is the fixed point. We define flip rate F(t) as the fraction of sites i such that 
and persistence P(t) as the fraction of sites i such that 
for all 
. The dynamic phase transitions to a synchronized state is studied above quantifiers. For 3 and 5 sites interaction, we find that at the critical point, 
with 
and 
with 
. They match the directed percolation (DP) class. Finite-size and off-critical scaling is consistent with DP class. For 2 and 4 site interactions, the exponent 
and behavior of P(t) at critical point changes. Furthermore, we observe logarithmic oscillations over and above power-law decay at the critical point for 4-site coupling. Thus multi-site interactions can lead to new universality class(es).
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
