Layered inhomogeneous Ising models with frustration on a square lattice

On the critical temperature of non-periodic Ising models on hexagonal lattices

“…This remarkably simple formula is similar to the critical point condition obtained on the square lattice for a simple layered model, i.e. for n = 1 [11]. It is easy to check that eq (13) contains, as a special case, the criticality condition for the homogeneous system [12].…”

“…Therefore in the non-periodic limit m → ∞ the critical temperature is explicitly known only for n = 1, i.e. for simple layered systems [11]. The homogeneous Ising model has also been solved exactly on triangular and honeycomb lattices for a long time [12], [13].…”

“…Therefore in the non-periodic limit m → ∞ the critical temperature is explicitly known only for n = 1, i.e. for simple layered systems [11].…”

Introduction to Conformal Invariance and Its Applications to Critical Phenomena

“…These systems display some kind of non-universal criticality. Another possibility, but leaving the domain of applicability of conformal invariance, is to let n grow faster than the lattice size [128], eventually ariving at random systems [253,315,328]. Quasiperiodic [107,38,184] and even some aperiodic [89,108,239] alterations do not change the universality class but the spectra of the quantum Hamiltonians display multifractal [162,192,151] features.…”

Phase Transition of Two-Dimensional Ising Models on the Honeycomb and Related Lattices with Striped Random Impurities

“…The criticality condition for both the models was derived in Refs. [29,15]. It is important that the partition function of the McCoy-Wu and the Shankar-Murthy models can be written as the largest eigenvalue, or the Lyapunov exponent in other words, of a product of random 2 × 2 matrices.…”