First- and second-order clustering transitions for a system with infinite-range attractive interaction

Area of Science:

• Statistical Mechanics
• Computational Physics

Background:

• Classical N-particle systems with infinite-range interactions exhibit complex phase behavior.
• Understanding phase transitions and ensemble equivalence is crucial in statistical mechanics.

Purpose of the Study:

• To investigate the phase transitions of a 2D classical N-particle system with infinite-range coupling.
• To explore the relationship between canonical and microcanonical ensembles for this system.
• To analyze the occurrence of negative specific heat and its implications.

Main Methods:

• Simulations of a Hamiltonian system with N classical particles in 2D.
• Analysis of phase transitions across different energy regimes.
• Comparison of canonical and microcanonical ensemble results.
• Extension of canonical analysis to metastable and unstable states.

Main Results:

• Observed distinct phases: clustered, homogeneous, and two-cluster.
• Identified second and first-order phase transitions depending on coupling strength (A).
• Demonstrated canonical analysis accurately describes microcanonical equilibrium, including negative specific heat regimes.
• Linked microcanonical stable states to Helmholtz free energy saddles within the spinodal region.

Conclusions:

• The system's phase diagram is rich and dependent on coupling strength.
• Ensemble equivalence holds even in the presence of negative specific heat when considering extended canonical states.
• The study provides insights into the behavior of systems with competing interactions and the subtleties of phase transitions.