Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagom\'{e} lattice

The two-dimensional Ising model on a distorted Kagom'{e} lattice is studied by means of exact solutions and the tensor renormalisation 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 $m=1\mathrm{/}3$ plateaux are observed in the magnetization curves for some couplings. The experimental data of susceptibility for the complex Co(N${}_3$)${}_2$(bpg)$\cdot$ DMF${}_{4\mathrm{/}3}$ are fitted with the TRG results, giving the couplings of the complex $J=22K$ and $J^{\mathrm{\prime }}=33K$.