Isometric fluctuation relations for equilibrium states with broken symmetry

Area of Science:

• Condensed matter physics
• Statistical mechanics

Background:

• Order parameter fluctuations are crucial for understanding phase transitions in finite-size systems.
• Broken symmetries in physical systems often lead to complex behaviors and emergent phenomena.

Purpose of the Study:

• To derive a general set of exact isometric fluctuation relations.
• To establish constraints on order parameter fluctuations in systems with broken symmetry.

Main Methods:

• Derivation of theoretical relations based on equilibrium statistical mechanics.
• Application and illustration of these relations to specific models like the Curie-Weiss and XY models.
• Analysis of magnetic systems and nematic liquid crystals under symmetry-breaking fields.

Main Results:

• A set of exact isometric fluctuation relations applicable to finite-size systems at equilibrium with broken symmetry.
• Demonstration of the general applicability of these relations across different condensed matter systems.
• Identification of implications for spontaneous symmetry breaking.

Conclusions:

• The derived fluctuation relations provide fundamental constraints for systems exhibiting broken symmetry.
• These relations offer a powerful tool for analyzing phase transitions and critical phenomena in diverse physical systems.
• The findings have broad implications for understanding symmetry breaking in condensed matter physics.