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Related Experiment Video

Updated: Jan 19, 2026

Phase Transitions and Effect of Intermolecular Forces

Phase Transitions and Effect of Intermolecular Forces

Invariant theory and orientational phase transitions.

Joseph Rudnick¹, Robijn Bruinsma^1,2

¹Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA.

Physical Review. E

|September 11, 2019

Summary

This summary is machine-generated.

Landau theory faces challenges with complex particle clusters and rotational symmetry breaking. A new geometrical method combined with visualization tools resolves issues of thermodynamic instability and non-physical invariants.

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Last Updated: Jan 19, 2026

Phase Transitions and Effect of Intermolecular Forces

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Sublimation, Deposition and Enthalpy Changes

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Melting and Freezing; Energetics of Melting and Fusion

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Area of Science:

Physics
Materials Science
Chemistry

Background:

Landau theory effectively models phase transitions involving rotational symmetry breaking.
Applications extend to orientational symmetry breaking in atomic and molecular clusters.
Complex particle clusters present challenges for Landau theory with higher-order symmetry breaking.

Purpose of the Study:

To address fundamental problems in applying Landau theory to complex particle clusters with rotational symmetry breaking.
To resolve issues of thermodynamic instability and proliferation of non-physical invariants.
To develop a robust method for analyzing symmetry breaking in complex systems.

Main Methods:

Utilized a geometrical method analyzing the space of invariants, adapted from Higgs potential symmetry breaking studies.
Integrated modern visualization tools to interpret complex symmetry breaking scenarios.
Applied the combined approach to numerical simulations of particle ordering on spherical surfaces and protein shell ordering.

Main Results:

Demonstrated a resolution to thermodynamic instabilities in expected ground states.
Provided a method to manage the proliferation of quartic invariants, distinguishing physical from non-physical ones.
Successfully applied the framework to analyze ordering in simulated particle clusters and protein shells.

Conclusions:

The combination of geometrical invariant analysis and visualization tools effectively overcomes limitations of Landau theory for complex rotational symmetry breaking.
This approach offers a powerful framework for studying symmetry breaking phenomena in diverse physical and biological systems.
The findings are applicable to understanding particle ordering in simulations and the structural organization of protein shells.