The paper by András Czirók and Tamás Vicsek explores the emergence of collective motion in self-propelled particle (SPP) systems, inspired by biological phenomena such as flocking and schooling. The authors study non-equilibrium models where particles interact by turning towards the average direction of their neighbors, leading to dynamics similar to Monte Carlo simulations of equilibrium ferromagnets. However, they find new types of phase transitions not present in equilibrium systems, particularly in one-dimensional (1D) SPP systems where an ordered phase exists at finite noise levels. The model consists of particles moving on a plane with periodic boundary conditions, updating their velocities based on the average direction of nearby particles plus random noise. Numerical simulations and analytical studies reveal a kinetic phase transition, with the order parameter scaling differently from equilibrium systems. The critical noise amplitude and exponents are distinct from those in equilibrium ferromagnets. In 3D, the behavior is similar to 2D, with a long-range ordered phase present for any density but vanishing at higher densities due to percolation. In 1D, the system exhibits ordered motion at low noise levels, which is not predicted by equilibrium models. The authors also develop a continuum theory to understand these phase transitions, showing that the stability of domain walls can lead to the ordering of the system. Overall, the study highlights the unique features of SPP systems, providing insights into the collective behavior of organisms in noisy environments.The paper by András Czirók and Tamás Vicsek explores the emergence of collective motion in self-propelled particle (SPP) systems, inspired by biological phenomena such as flocking and schooling. The authors study non-equilibrium models where particles interact by turning towards the average direction of their neighbors, leading to dynamics similar to Monte Carlo simulations of equilibrium ferromagnets. However, they find new types of phase transitions not present in equilibrium systems, particularly in one-dimensional (1D) SPP systems where an ordered phase exists at finite noise levels. The model consists of particles moving on a plane with periodic boundary conditions, updating their velocities based on the average direction of nearby particles plus random noise. Numerical simulations and analytical studies reveal a kinetic phase transition, with the order parameter scaling differently from equilibrium systems. The critical noise amplitude and exponents are distinct from those in equilibrium ferromagnets. In 3D, the behavior is similar to 2D, with a long-range ordered phase present for any density but vanishing at higher densities due to percolation. In 1D, the system exhibits ordered motion at low noise levels, which is not predicted by equilibrium models. The authors also develop a continuum theory to understand these phase transitions, showing that the stability of domain walls can lead to the ordering of the system. Overall, the study highlights the unique features of SPP systems, providing insights into the collective behavior of organisms in noisy environments.