• 75.10.Jm;
  • 75.30.Kz;
  • 77.90.+k


The phase diagrams of a ferroelectric small particle described by the transverse Ising model (TIM) are investigated by the use of two theoretical frameworks, namely the standard mean-field theory and the effective-field theory corresponding to the Zernike approximation. The particle is represented by a two-dimensional array of pseudo-spins with two types of exchange interactions (J in bulk and JS on the surface) and two types of transverse fields (Ω in the bulk and ΩS on the surface). We study the phase diagrams of this model, changing the size S of the particle and the ratios of JS/J and ΩS/Ω. We find that the critical behaviors are a little different from those found for the phase diagrams of ferroelectric thin films described by the TIM. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)