Geometric Phase Transitions with Emergent Complexity

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Geometric phase transitions, characterized by complex geometric structures, represent a significant challenge in condensed matter physics. This paper proposes a novel framework for analyzing these transitions, focusing on the emergence of complexity through subtle geometric interactions. We introduce a "geometric fingerprint" – a quantifiable measure of the system's geometric structure – and demonstrate its potential to provide a deeper understanding of the transition mechanism. The core claim is that a rigorous analysis of geometric phase transitions, guided by this fingerprint, can yield insights into the underlying dynamics and ultimately, the emergence of complex behavior. This work contributes to the field by offering a potentially more insightful and mathematically rigorous approach to understanding these fundamental phenomena.

DOI: 10.5281/zenodo.22578287

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