Finite-Size Thermodynamics of the Two-Dimensional Dipolar Q-Clock Model

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Thermodynamics

Background:

• The 2D dipolar Q-state clock model is crucial for understanding magnetic systems with competing interactions.
• Investigating small lattices with free boundaries is essential for finite-size scaling and identifying emergent phenomena.
• Long-range dipolar interactions significantly influence the low-energy states and thermodynamic properties.

Purpose of the Study:

• To conduct a controlled thermodynamic study of the 2D dipolar Q-state clock model on small square lattices.
• To resolve energy spectra and degeneracies for various Q values and lattice sizes.
• To identify novel thermodynamic signatures induced by dipolar anisotropy and their dependence on system parameters.

Main Methods:

• Exhaustive enumeration of all possible states for small lattices.
• Noise-free evaluation of canonical thermodynamic observables.
• Systematic variation of the dipolar interaction to exchange interaction ratio (α=D/J).

Main Results:

• Ground-state level crossings manifest as exact zeros in specific heat at T→0.
• The shape of Schottky anomalies reveals details about the degeneracy structure of low-energy states, influenced by lattice parity.
• A symmetry-driven crossover is observed: Q=2,4 models show sharp critical points, while Q≥6 models exhibit smooth energy landscapes and thermal maxima.

Conclusions:

• Dipolar interactions alone can generate non-trivial, critical-like caloric behavior in mesoscopic magnetic systems (e.g., 3x3 lattices).
• Lattice parity and discrete rotational symmetry are key organizing principles for the thermodynamics of these systems.
• The findings provide exact finite-size benchmarks relevant for van der Waals nanomagnets and artificial spin-ice systems.