Thermodynamics of the Spin Square

Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an example of a completely integrable system, in the double sen...

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Bibliographic Details
Published in:Few-body systems 2023-04, Vol.64 (2), p.16, Article 16
Main Authors: Schmidt, Heinz-Jürgen, Schröder, Christian
Format: Article
Language:English
Subjects:
Antiferromagnetism
Atomic
Hadrons
Heat
Heavy Ions
Low temperature
Molecular
Nuclear Physics
Numerical analysis
Optical and Plasma Physics
Particle and Nuclear Physics
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum mechanics
Quantum numbers
Thermodynamics
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Summary:Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an example of a completely integrable system, in the double sense: quantum mechanical and classical. However, this does not automatically imply that the thermodynamic quantities of the classical system can also be calculated explicitly. In this work, we derive analytical expressions for the density of states, the partition function, specific heat, entropy, and susceptibility. These theoretical results are confirmed by numerical tests. This allows us to compare the quantum mechanical quantities for increasing spin quantum numbers s with their classical counterparts in the classical limit s → ∞ . As expected, a good agreement is obtained, except for the low temperature region. However, this region shrinks with increasing s , so that the classical state variables emerge as envelopes of the quantum mechanical ones.
ISSN:1432-5411
0177-7963
1432-5411
DOI:10.1007/s00601-023-01797-x