The Ising model describes a many-body interacting spin system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins with $Z_{2} $ symmetry, the phenomena revealed in Ising systems may afford us lessons for other types of interactions in nature. In this talk, I would like to first focus on the mathematical structure of the three-dimensional (3D) Ising model, regarding to the Clifford algebra representation. It is revealed in the Clifford algebra representation that there exist many internal factors in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space. They result in the non-locality as well as the long-range entanglement between spins in the 3D Ising model. I would like to emphasize the important roles of the Clifford algebra representation on solving the exact solution of the ferromagnetic 3D Ising model and determining the lower bound of the computational complexity of the spin-glass 3D Ising model. Then, I will establish the framework of topological quantum statistical mechanics, with respect to the mathematical aspects (topology, algebra and geometry) and physical features (Jordan-von Neumann-Wigner framework, time average, ensemble average and quantum-mechanical average). This is done by a generalization of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan-von Neumann-Wigner framework. It is necessary to account the time average of the ensemble average and the quantum-mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time in the topological quantum field theories.