The Ising model with a periodic spin-lattice coupling on the triangular lattice

In this work, we study and evaluate the impact of a periodic spin-lattice coupling in an Ising-like system on a 2D triangular lattice. Our proposed simple Hamiltonian considers this additional interaction as an effect of preferential phonon propagation direction augmented by the symmetry of the underline lattice. The simplified analytical description of this new model brought us consistent information about its ground state and thermal behavior, and allowed us to highlight a singularity where the model behaves as several decoupled one-dimensional Ising systems. A thorough analysis was obtained via numerical simulations using the Wang-Landau Monte Carlo method that estimates the density of states g(E) to explore the phase diagram and other thermodynamic properties of interest. Also, we used the finite size scaling technique to characterize the critical exponents and the nature of the phase transitions that, despite the strong influence of the spin-lattice coupling, turned out to be within the same universality class as the original 2D Ising model.