Separating Energy and Entropy Contributions to the Hexatic-Liquid Transitions in Two-Dimensional Repulsive Systems

TL;DR

This study decomposes the Helmholtz free energy in two-dimensional repulsive systems to reveal how energy and entropy competition determines whether melting transitions are first-order or continuous, providing a universal thermodynamic principle.

Contribution

It introduces a universal framework based on free energy curvature to explain the nature of 2D melting transitions, linking energy and entropy contributions to transition types.

Findings

First-order transitions occur when entropy dominates and is concave.

Continuous transitions happen when entropy is convex and vibrational entropy drives concavity.

At zero temperature, the transition becomes continuous as entropic effects vanish.

Abstract

Over the past decades, research on two-dimensional melting has established that both first-order and continuous hexatic-liquid transitions can occur, influenced by various factors in the potential energy and system details. The fundamental thermodynamic origins of this sensitivity remains elusive. Here, by decomposing the Helmholtz free energy across three representative repulsive systems, we reveal a universal competition between energy and entropy that dictates the melting pathway. The energetic contribution consistently imparts convexity to the free energy, whereas entropy imparts concavity. A first-order transition occurs when concave entropy dominates; otherwise, the transition is continuous. Further decomposition shows that vibrational entropy drives the concave total entropic curvature, while the configurational entropy's curvature switches from convex (first-order) to concave (continuous), mirroring defect proliferation measured by Shannon entropy. The convexity of the energy is dominated by the inherent potential, with minimal vibrational influence. Finally, we predict and verify that the first-order transition becomes continuous at zero temperature, where entropic effects vanish. Our work establishes the curvature of different thermodynamic quantities as a fundamental principle for understanding the nature of two-dimensional melting.