Bond Dilution Effects on Bethe Lattice the Spin-1 Blume–Capel Model

Abstract

The bond dilution effects are investigated for the spin-1 Blume–Capel model on the Bethe lattice by using the exact recursion relations. The bilinear interaction parameter is either turned on ferromagnetically with probability p or turned off with probability 1 – p between the nearest-neighbor spins. The thermal variations of the order-parameters are studied in detail to obtain the phase diagrams on the possible planes spanned by the temperature (T), probability (p) and crystal field (D) for the coordination numbers q = 3, 4, and 6. The lines of the second-order phase transitions, Tc-lines, combined with the first-order ones, Tt-lines, at the tricritical points (TCP) are always found for any p and q on the (T, D)-planes. It is also found that the model gives only Tc-lines, Tc-lines combined with the Tt-lines at the TCP’s and only Tt-lines with the consecutively decreasing values of D on the (T, p)-planes for all q.

Super slowing down in the bond-diluted Ising model

“…In the Ising model, the impurities have been implemented in terms of randomly placed nonmagnetic spins (site-diluted Ising model) [3][4][5][6][7] or missing interactions (bond-diluted Ising model) [8][9][10][11][12]. The inclusion of any kind of randomness into the system can have significant effects on its critical properties [13]. For instance, a new universality class was found in the three-dimensional bond-diluted Ising model [14,15], and complex logarithmic corrections for the equilibrium properties were observed [7,16].…”

Super slowing down in the bond-diluted Ising model

“…In the Ising model, the impurities have been implemented in terms of randomly placed nonmagnetic spins (site-diluted Ising model) [4][5][6][7][8] or missing interactions (bond-diluted Ising model) [9][10][11][12][13]. The inclusion of any kind of randomness into the system can have significant effects on its critical properties [14]. For instance, a new universality class was found in the three-dimensional bond-diluted Ising model [15,16], and complex logarithmic corrections for the equilibrium properties were observed [8,17].…”