Phase diagrams for the bond- and site-diluted transverse Ising model

The transverse spin-1 Ising model with random interactions

“…In addition to the study of the pure systems, site-diluted systems [17][18][19], random bond models [17,18,20], amorphous magnets [21], semi-infinite systems with a variety of surfaces [22][23][24][25], thin films [26,27], superlattices [28], and multilayers [29] have been studied. The effective field theory has also been extended to the spin-1 system [30][31][32][33][34] and to the mixed spin-1 2 and spin-1 systems [35][36][37][38].…”

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

“…[56]. The diluted spin-1/2 transverse Ising model has been investigated by Fittipaldi et al [57]; the present system is very similar to those of the spin-1/2 case. In Fig.…”

A new effective field theory for spin-S (S<=1) dilute Ising ferromagnets

“…where the coefficients K n , (n = 1, ..., 4) and A l , (l = 1, ..., 3) are given in Eqs. ( 13) and (18), respectively. On the other hand, corresponding to Eq.…”

“…They have also found that this concentration depends on the coordination number of the lattice. After this seminal work of Sato et al [5], much attention has been paid to site dilution problem and the situation has been handled by a wide variety of techniques such as Bethe-Peierls-Weiss (BPW) method [6], renormalization group (RG) technique [7][8][9][10], correlated effective field theory (CEFT) [11][12][13], effective field theory (EFT) based on decoupling (or Zernike [14]) approximation (DA) [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], an integral representation method [34], Monte Carlo (MC) simulation technique [35][36][37][38], Bogoliubov inequality approach [39], Bethe-Peierls approximation (BPA) [40], finite cluster approximation (FCA) which gives results identical to those obtained by EFT for a one spin cluster [41][42][43][44], third order Matsudaira approximation [45], EFT with probability distribution technique [46][47]...…”