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Dettagli Bibliografici
Autore principale: delpech, maxime
Natura: Recurso digital
Lingua:inglese
Pubblicazione: Zenodo 2025
Soggetti:
Accesso online:https://doi.org/10.5281/zenodo.17778979
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Sommario:
  • <p> We introduce Distribution–Metric Geometry (DMG), a geometric framework for analyz<br>ing phase transitions directly in the space of empirical probability distributions generated<br> by microscopic models. Instead of focusing on model-specific order parameters, DMG con<br>structs a multi-metric embedding of each model into an information-geometric manifold.<br> Phase transitions then appear as geometric events: sudden reorientation of the trajectory in<br> metric space, peaks in geometric speed and curvature, and temporary expansion of intrinsic<br> dimensionality. Across three classical 2D lattice models (Villain, XY, Ising), DMG reveals<br> that their trajectories in metric space require, respectively, one, two, and three principal ge<br>ometric modes. These intrinsic dimensions are stable under the choice of metrics and system<br> size, and behave as robust geometric invariants of each model. . The framework is model<br>agnostic and extends naturally to complex systems where traditional order parameters are<br> unknown or purely topological.</p>