Pattern phase transition of spin particle lattice system

To better understand the pattern phase transition of both physical and biological systems, we investigate a two-dimensional spin particle lattice system using statistical mechanics methods together with XY model governed by Hamiltonian equations of motion. By tweaking the coupling strength and the intensity of the generalization field, we observe phase transitions among four patterns of spin particles, i.e., vortex, ferromagnet, worm and anti-ferromagnet. In addition, we analyze the effect of space boundaries on the formations of vortex and worm. Considering the inherent dynamics of individual particles, we revealed the forming mechanism of such phase transitions, which provides a new perspective for understanding the emergence of phase transition of spin particles systems.