The one-dimensional Ising model is typically analyzed as an open chain system with free ends, but when an external field is introduced, it is often treated with cyclic boundary conditions. The equivalence of these methods is questioned, particularly regarding the computational costs associated with the quantum treatment of the transverse-field Ising model, which increases exponentially with the number of spins. For infinite 1D lattices, the classical transverse-field Ising model can be effectively approximated using Maximal Entropy Random Walk (MERW). Additionally, the 2D classical Ising model with finite width can be solved analytically using MERW under cyclic boundary conditions. Understanding these methods and their implications is crucial for advancing computational techniques in statistical physics.