Magnetocaloric effect for a $Q$-clock type system

TL;DR

This study investigates the magnetocaloric effect in a $Q$-state clock model, analyzing how entropy and magnetic field variations influence cooling efficiency across different lattice sizes and state configurations.

Contribution

It provides the first detailed Monte Carlo simulation analysis of the MCE in $Q$-state clock models for various $Q$ and lattice sizes, highlighting optimal conditions for maximum effect.

Findings

Maximized MCE at specific $Q$ values depending on lattice size.

Identification of phase transition points affecting MCE.

Quantitative relationship between magnetic field variation and entropy change.

Abstract

In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with $Q$ possible orientations, known as the ``$Q$-state clock model". When the $Q$-state clock model has $Q\geq 5$ possible configurations, it presents the famous Berezinskii Kosterlitz Thouless (BKT) phase associated with vortices states. We calculate thermodynamic quantities using Monte Carlo simulations for even $Q$ numbers, ranging from $Q=2$ to $Q=8$ spin orientations per site in a lattice. We use lattices of different sizes with $L\times L = 8^{2}, 16^{2}, 32^{2}, 64^{2}, \text{and}\ 128^{2}$ sites, considering free boundary conditions and an external magnetic field varying between $B = 0$ and $B=1$ 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 $Q$ that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the $Q$-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 mechanics and related fields.