Otto Engine for the q-State Clock Model

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Thermal-magnetic engines offer potential for energy conversion.
• Spin models are crucial for understanding magnetic phenomena and their thermodynamic implications.

Purpose of the Study:

• To investigate the performance of a thermal-magnetic Otto-type engine.
• To analyze the thermodynamic quantities of the q-state clock model as a working substance.
• To explore the influence of magnetic phases on engine performance.

Main Methods:

• Exact calculation of the partition function for small lattices (3x3).
• Application of the mean-field approximation for larger lattices.
• Analysis of thermodynamic quantities across different q-values (2, 4, 6, 8).

Main Results:

• The q=4 clock model demonstrated the highest work extraction.
• The Ising model (q=2) exhibited the lowest performance.
• Work extraction is higher during ferromagnetic-to-paramagnetic transitions compared to BKT-to-paramagnetic transitions.
• Increasing lattice size decreased work extraction for all q-values.

Conclusions:

• The choice of working substance (q-state clock model) significantly impacts engine performance.
• Engine efficiency is intrinsically linked to the underlying magnetic phase transitions.
• Lattice size plays a critical role in determining the work output of the thermal-magnetic engine.