The dynamic real-space renormalization group of Mazenko and Valls is applied to the zero-field ferromagnetic Ising model on the triangular lattice. Renormalization equations valid for all temperatures above the critical temperature
Tc are derived for the susceptibility, specific heat, structure factor, and correlation length. The magnetization is found for
T<Tc. The critical exponents and amplitudes for these quantities are calculated. The agreement between the known static properties and the renormalization-group results is good to excellent, and shows that this renormalization-group method can accurately calculate nonuniversal, as well as universal, quantities on different lattices. The computed dynamic structure factor, however, exhibits nonmonotonic behavior as a function of temperature. This nonmonotonic behavior is conjectured to be due to approximations in determining the expansion parameters.
We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.
The two-dimensional Ising model on a distorted kagome lattice is studied by means of exact solutions and the tensor renormalization-group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as ferromagnetic, ferrimagnetic, and paramagnetic phases, along with the second-order phase transitions, have been identified. The TRG results are quite accurate and reliable in comparison to the exact solutions. In a magnetic field, the magnetization
(m), susceptibility, and specific heat are studied by the TRG algorithm, where the
m=1/3 plateaux are observed in the magnetization curves for some couplings. The experimental data of susceptibility for the complex $\text{Co}{({\text{N}}_{3})}_{2}(\text{bpg})\ensuremath{\cdot}{\text{DMF}}_{4/3}$ are fitted with the TRG results, giving the couplings of the complex
J=22 K and ${J}^{\ensuremath{'}}=33\text{ }\text{K}$.