Thermodynamics of Small Magnetic Particles

VOGEL, EUGENIO; VARGAS, PATRICIO; SARAVIA, GONZALO; VALDES, JULIO; RAMIREZ-PASTOR, ANTONIO; CENTRES, PAULO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Año: 2017 vol. 19

1099-4300

In the present paper, we discuss the interpretation of some of the results of thethermodynamics in the case of very small systems. Most of the usual statistical physics is donefor systems with a huge number of elements in what is called the thermodynamic limit, but not all ofthe approximations done for those conditions can be extended to all properties in the case of objectswith less than a thousand elements. The starting point is the Ising model in two dimensions (2D)where an analytic solution exits, which allows validating the numerical techniques used in the presentarticle. From there on, we introduce several variations bearing in mind the small systems such as thenanoscopic or even subnanoscopic particles, which are nowadays produced for several applications.Magnetization is the main property investigated aimed for two singular possible devices. The size ofthe systems (number of magnetic sites) is decreased so as to appreciate the departure from the resultsvalid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the realityof small particles; 1D, 2D and 3D systems are examined to appreciate the differences establishedby dimensionality is this small world; upon diluting the lattices, the effect of coordination number(bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q = 2degrees of freedom, we combine previous results with the supplementary degrees of freedom comingfrom the variation of q up to q = 20. Most of the previous results are numeric; however, for thecase of a very small system, we obtain the exact partition function to compare with the conclusionscoming from our numerical results. Conclusions can be summarized in the following way: the lawsof thermodynamics remain the same, but the interpretation of the results, averages and numericaltreatments need special care for systems with less than about a thousand constituents, and this mightneed to be adapted for different properties or devices.