Impact of Higher-Order Interactions on Collective Motion

This dataset contains all simulation data, simulation source code, and Python plotting scripts required to reproduce every figure in the paper "Impact of Higher-Order Interactions on Collective Motion: A Modified Vicsek Model with Triadic Alignment" (submitted to Physical Review Letters).

The paper introduces a generalized Vicsek model in which standard pairwise alignment is replaced or mixed with a triadic (three-body) interaction via a mixing parameter α. Using agent-based simulations and mean-field theory, we show that pure triadic alignment (α=0) induces a discontinuous (first-order) order–disorder phase transition, while the standard pairwise Vicsek model (α=1) exhibits a continuous (second-order) transition at the same system sizes.

The dataset is organized into six folders, one per figure:

Main-Fig1: Schematic diagram of the model (draw.io source file)

Main-Fig2: Order parameter, susceptibility, and Binder cumulant comparing SVM and HOVM at density ρ=8

Main-Fig3: Dependence of the transition on particle density ρ and mixing parameter α, including a heat map of the order parameter in the (α,η) plane

Main-Fig4: Finite-size scaling analysis and four independent signatures of the first-order transition: susceptibility peak, Binder cumulant minimum, double-well free energy, and hysteresis

Main-Fig5: Mean-field fixed points of the self-consistency equation for α=0 and α=1

Fig-Appendix-A: Integrated autocorrelation time of the order parameter as a function of noise amplitude for five system sizes

Each folder contains a README file with a full description of the data format, simulation parameters, and instructions for reproducing the figures. Simulation codes are provided in both C++ (CPU, OpenMP) and CUDA (GPU) versions. Plotting scripts are written in Python and require numpy and matplotlib.

Keywords: active matter, collective motion, Vicsek model, higher-order interactions, phase transition, first-order transition, self-propelled particles, agent-based simulation