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Phase transitions - boiling water, superconductivity, ferromagnetism - are among the clearest examples of abrupt change in physical systems. In this note, I examine them through a structural lens: as regime boundaries where the persistence conditions of one descriptive framework fail and a new coherent regime emerges.

Rather than replacing existing theory, the goal is to show how a focus on relational coherence and threshold behavior can clarify when stable organization persists or transitions.

The critical point is not just a mathematical singularity - it is a structural boundary where the old description loses validity while the system reorganizes into a new coherent regime.

Phase Transitions as Regime Boundaries: Structural Persistence and Critical Behavior in Relational Field Theory

**https://doi.org/10.17605/OSF.IO/VCNUQ**

Series Progress:

  1. Mathematical Conditions for Regime Failure in Relational Field Theory
  2. Phase Transitions as Regime Boundaries ← current paper
  3. Turbulence as Regime Breakdown
  4. Boundary-Constrained Persistence
  5. The Planck Regime as a Boundary Intersection
  6. Relational Field Theory: Structural Program Overview

Comments and constructive feedback welcome.

#RelationalFieldTheory #PhaseTransitions #ComplexSystems #Physics

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