Magnetic Properties and Phase Transitions in a Diluted Ferromagnet: Ising, XY, and Heisenberg Models

Abstract

The magnetic properties and phase transition of a ferromagnetic spin-S disordered diluted thin film with a face-centred cubic lattice are investigated using the high-temperature series expansion technique extrapolated with Pade approximant method for Heisenberg, XY and Ising models. The reduced critical temperature of the system \(\tau_{\mathrm{c}}=\frac{k_{\mathrm{B}}T_{\mathrm{c}}}{2S(S+1)J_{\mathrm{b}}}\) is studied as the function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces Jb,Js and J⊥, respectively. It is found that τc increases with the exchange interactions of surface. The magnetic phase diagrams (τc versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures Tc(L) from the bulk value \((\frac{T_{\mathrm{c}}(\infty )}{T_{\mathrm{c}}(L)}-1)\) can be described by a power law L−λ, where λ is the inverse of the correlation length exponent.