Abstract
This present work explores the performance of a thermal–magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the state clock model. We obtain all the thermodynamic quantities for the q = 2, 4, 6, and 8 cases in a small lattice size ( with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the case, while the performance for the Ising model () is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of q presented in this study.
Highlights
We have addressed the possibility of operating an Otto engine whose working substance is an interacting spin system corresponding to the q-state clock model
We have calculated and analyzed the thermodynamics of the system exactly by obtaining all the accessible microstates of the system, while for larger lattices, we have performed the calculations through the mean-field approximation
The working substance used presents one or two phase transitions depending on the degree of freedom of the spin; the selection of the operating range of the motor cannot be arbitrarily selected, and in our study, we have placed it for the Ising model (q = 2) and q = 4 from an ordered phase to a disordered phase, while for q = 6 and q = 8, it is from a vortex phase (BKT phase) to a disordered phase
Summary
The Otto cycle, widely used by the automotive industry, is today one of the most studied cycles theoretically and experimentally in thermodynamics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Each location of a maximum of the specific heat on the temperature axis will represent a value for a so-called critical temperature It has been shown [35,36,37,38,39,40] (in the absence of an external magnetic field) that for the q-clock state model, values q ≥ 5 (where q represents the number of possible orientations that the spins can take), the specific heat presents two maxima. We propose to study the work and efficiency of an Otto engine whose working substance is an interacting spin system based on the well-known q-state clock model. For this purpose, a complete analysis of the thermodynamics of small lattice systems will be made by exact calculations, and the mean-field approximation will be used for large lattice sizes.
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