2012/05/04 by Dalía S. Bertoldi, Eduardo M. Bringa, E. N. Miranda · 1 citation
Physics and Astronomy · Earth and Planetary Sciences · Mathematics · #Theoretical and Computational Physics #nanoparticles nucleation surface interactions #Quantum many-body systems #Ising model #Scaling #Monte Carlo method #Magnetization #Statistical physics #Exponent #Curie temperature #Mean field theory #Physics #Condensed matter physics #Mathematics #Magnetic field #Ferromagnetism #Quantum mechanics #Geometry #Statistics
paper · doi:10.1088/0953-8984/24/22/226004
openalex publication_date 2012/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The Ising model for finite systems, e.g. for clusters of different sizes and crystal lattices, was solved analytically by the mean field approach. The magnetization was calculated from the number of accessible microstates, using the gamma function and its derivatives, unlike the usual solution in the microcanonical which uses the Stirling approximation. We determined a scaling exponent of ∼1/3, which shows how the Curie temperature decreases with decreasing nanoparticle size. Moreover, the model predicts the behaviour of surface and core regions and it explains in simple terms several effects previously observed in experiments and Monte Carlo simulations of small magnetic systems.