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

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 J b,J s and J ⊥, respectively. It is found that τ c increases with the exchange interactions of surface. The magnetic phase diagrams (τ c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T c(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.