Non-extensive thermodynamics of transition-metal nanoclusters

TL;DR

This paper explores the thermodynamic properties of transition-metal nanoclusters using non-extensive statistics, revealing significant differences from traditional models, especially for small clusters, through calculations of specific heat, magnetization, and susceptibility.

Contribution

It introduces non-extensive statistical calculations for nanoclusters modeled as Hubbard dimers, highlighting differences from classical thermodynamics for small systems.

Findings

Thermodynamic properties vary significantly for small clusters compared to macroscopic systems.

Non-extensive statistics alter the temperature and magnetic-field dependence of thermodynamic quantities.

Results differ notably from those predicted by Boltzmann-Gibbs statistics for small M values.

Abstract

In recent years, much study has been made by applying the {\it non-extensive statistics} (NES) to various non-extensive systems where the entropy and/or energy are not necessarily proportional to the number of their constituent subsystems. The non-extensivity may be realized in many systems such as physical, chemical and biological ones, and also in small-scale nanosystems. After briefly reviewing the recent development in nanomagnetism and the NES, I have discussed, in this article, NES calculations of thermodynamical properties of a nanocluster containing noninteracting $M$ dimers. With bearing in mind a transition-metal nanocluster, each of the dimers is assume to be described by the two-site Hubbard model ({\it a Hubbard dimer}). The temperature and magnetic-field dependences of the specific heat, magnetization and susceptibility have been calculated by changing M=1, 2, 3 and $\infty$, results for $M=\infty$ corresponding to those of the conventional Boltzman-Gibbs statistics (BGS). It has been shown that the thermodynamical property of nanoclusters containing a small number of dimers is considerably different from that of macroscopic counterparts calculated within the BGS The specific heat and susceptibility of spin dimers described by the Heisenberg model have been discussed also by employing the NES.