Distribution of RKKY coupling value in 1D crystal with disorder. Specific heat in XY model

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Disorder in 1D crystals localizes charge carriers.
• Perturbative calculations of RKKY interaction are invalid in 1D due to localization.
• RKKY interaction in 2D/3D systems can be calculated perturbatively, showing high magnitudes due to interference.

Purpose of the Study:

• To describe the indirect exchange interaction (RKKY) in 1D disordered systems.
• To calculate the heavy-tail distribution function for RKKY interaction in 1D.
• To investigate the impact of disorder-induced RKKY randomness on system observables, specifically specific heat.

Main Methods:

• Analytical calculation of RKKY interaction in 1D disordered systems.
• Derivation of a heavy-tail distribution function for RKKY interaction.
• Calculation of specific heat for the 1D XY model with disorder.

Main Results:

• RKKY interaction in 1D disordered systems is a random variable with a heavy-tail distribution.
• The calculated heavy-tail distribution applies on the scale of carrier localization length.
• Disorder eliminates the characteristic peak in specific heat temperature dependence for the 1D XY model.

Conclusions:

• The indirect exchange interaction in 1D disordered systems is not characterized by a single magnitude but by a heavy-tail distribution.
• The absence of a characteristic RKKY interaction value significantly modifies observable properties of these systems.
• Disorder fundamentally alters thermodynamic properties like specific heat by removing characteristic energy scales.