Pseudo-Goldstone Modes and Dynamical Gap Generation from Order by Thermal Disorder

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• Accidental ground state degeneracies, not caused by global symmetries, are typically unstable and lifted by fluctuations.
• This lifting often results in long-range order via the order-by-disorder (ObD) phenomenon.
• Distinguishing ObD from conventional energetic selection in real materials lacks clear signatures.

Purpose of the Study:

• To identify a unique, qualitative signature for order by thermal disorder (ObTD) in materials.
• To characterize the temperature dependence of the fluctuation-induced pseudo-Goldstone gap in ObTD systems.
• To demonstrate this signature in a minimal two-dimensional model.

Main Methods:

• Utilizing spin-dynamics simulations.
• Employing self-consistent mean-field calculations.
• Analyzing a minimal two-dimensional model: the ferromagnetic Heisenberg-compass model on a square lattice.

Main Results:

• A characteristic temperature dependence of the pseudo-Goldstone gap was identified as a signature for ObTD.
• In the studied model, the pseudo-Goldstone gap (Δ) exhibits a square-root-of-temperature (√T) scaling at low temperatures.
• A power-law temperature dependence of the gap is established as a general consequence of ObTD.

Conclusions:

• The fluctuation-induced pseudo-Goldstone gap's temperature dependence provides a distinct signature for ObTD.
• A simple model of a particle in an effective potential can capture the key physics of ObTD.
• This work offers a new method for detecting and characterizing ObD phenomena in physical systems.