What question did this study set out to answer?

The research aims to establish a geometric framework for analyzing phase transitions through value functions and rupture operators.

March 21, 2026Open Access

Phase Transitions as Geometric Ruptures: A Variational Perspective

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Proposes a new geometric framework to understand phase transitions, suggesting a unified interpretation across multiple domains.

The research aims to establish a geometric framework for analyzing phase transitions through value functions and rupture operators.
Developed a concave value function Ψ(λ) to represent phase transitions.
Introduced rupture operators to capture discrete transitions between configurations.
Analyzed the significance of non-differentiable points in the value function.
Illustrated the framework using Landau theory and the LASSO regularization path.
Identified regime changes at non-differentiable points of the value function.
Established relationships between singularities and the coexistence of multiple minimizers.
Demonstrated a common structure underlying various phase transitions and regime changes.

Luc de Veigy (2026) studied this question.

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