Magnetocaloric Effect for a <i>Q</i>-Clock-Type System
In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with <i>Q</i> possible orientations, known as the “<i>Q</i>-state clock model”. When the <i>Q</i>-state clock model has <inline-formula>&...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/1/11 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with <i>Q</i> possible orientations, known as the “<i>Q</i>-state clock model”. When the <i>Q</i>-state clock model has <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>≥</mo><mn>5</mn></mrow></semantics></math></inline-formula> possible configurations, it presents the famous Berezinskii–Kosterlitz–Thouless (BKT) phase associated with vortex states. We calculate the thermodynamic quantities using Monte Carlo simulations for even <i>Q</i> numbers, ranging from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>8</mn></mrow></semantics></math></inline-formula> spin orientations per site in a lattice. We use lattices of different sizes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mi>L</mi><mo>×</mo><mi>L</mi><mo>=</mo><msup><mn>8</mn><mn>2</mn></msup><mo>,</mo><msup><mn>16</mn><mn>2</mn></msup><mo>,</mo><msup><mn>32</mn><mn>2</mn></msup><mo>,</mo><msup><mn>64</mn><mn>2</mn></msup><mo>,</mo><mi>and</mi><mspace width="4pt"></mspace><msup><mn>128</mn><mn>2</mn></msup></mrow></semantics></math></inline-formula> sites, considering free boundary conditions and an external magnetic field varying between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>1.0</mn></mrow></semantics></math></inline-formula> in natural units of the system. By obtaining the entropy, it is possible to quantify the MCE through an isothermal process in which the external magnetic field on the spin system is varied. In particular, we find the values of <i>Q</i> that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the <i>Q</i>-state clock model in areas such as percolation theory, neural networks, and biological systems, where multi-state interactions are essential, our study provides a robust framework in applied quantum mechanics, statistical physics, and related fields. |
|---|---|
| ISSN: | 1099-4300 |