2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92975The periodic boundary conditions changed the plane square-lattice Ising model to the torus-lattice system which restricts the spin-projection orientations. Only two of the three important spin-projection orientations, parallel to the x-axis or to the y-axis, are suited to the torus-lattice system. The infinitesimal difference of the free-energies of the systems between the two systems mentioned above makes their critical temperatures infinitely close to each other, but their topological fundamental groups are distinct.7 pages,submitted to EJTP,the word"spin orientation" is substituted by the word "spin-projection orientation"Quantum Physicstext