Characterizing phase transitions through the pattern language

The central task of condensed matter physics is to investigate the physical properties of macroscopic systems composed of a vast number of interacting particles and the changes in their states. Interactions are the root cause of rich physical phenomena. Based on the fundamental question of “what is the relationship between the motions of particles if they interact”, the paper introduces a novel theoretical framework: pattern language. A “pattern” is defined as an ordered organizational structure formed by the “in-phase” and “out-of-phase” relationships between particles, arising from interactions. The paper applies this approach to the study of phase transitions using the one-dimensional axial next-nearest-neighbor Ising model as a concrete example. The results indicate that “patterns” can intuitively characterize various types of order in the system and can be regarded as generalized order parameters, offering a new perspective and language for understanding and describing the collective effects of interactions.