Exact results of a general spin-1 model on 2D decorated lattices

Equivalence between non-bilinear spin-S Ising model and Wajnflasz model

“…The critical points for honeycomb (γ = 3), square (γ = 4), and triangle (γ = 6) lattice can be fully recovered, which is consistent with the results previously obtained by Mi and Yang [4], for the case of spin-1 Ising model (for detail see table I of reference [4]). However our result is quite general and is valid for any spin-S and for any coordination number.…”

“…It is worth to notice the frustration properties of those model was not discussed by Mi and Yang [4].…”

“…Using the above result (44), we can obtain a residual entropy for the spin-1 Ising model discussed by Mi and Yang [4], the first model has residual entropy given by S = ln(2) while the second model has no residual entropy. It is worth to notice the frustration properties of those model was not discussed by Mi and Yang [4].…”

Phase diagrams of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice

“…Finally, it should be stressed that the approach based on a rigorous mapping with the spin-1 BEG model has been up to now only rather rarely used to obtain exact results due to the lack of corresponding exact solutions for the equivalent spin-1 BEG model [39][40][41][42]. From this point of view, it is noteworthy that the present exact formalism can be rather easily extended to investigate models with a more complicated Hamiltonian.…”

Exact Results of the Mixed-Spin Ising Model on a Decorated Square Lattice With Two Different Decorating Spins of Integer Magnitudes

“…It should be stressed, nevertheless, that a precise treatment of two-dimensional Ising models is often connected with considerable difficulties, which relate to the usage of sophisticated mathematical methods when applying them to more complex models describing, for instance, spin systems with interactions beyond nearest neighbors, 3-7 frustrated spin systems, [8][9][10] or higher-spin models with (or without) single-ion anisotropy and biquadratic interactions. [11][12][13][14][15][16][17][18][19][20][21][22] Up to now, exact results for Ising models on the square, 1 triangular and honeycomb, [23][24][25][26][27] kagomé, 28 extended kagomé, 29,30 bathroom-tile, [31][32][33][34][35] orthogonaldimer 36 and ruby 37 lattice, as well as on various irregular 2D lattices, such as Union Jack (centered square), [38][39][40][41][42][43][44] pentagonal, 45 square-kagomé, 46 or two topologically distinct square-hexagonal 47,48 lattices, have been obtained.…”