  There is no an exact solution to three-dimensional (3D) finite-size Ising
model (referred to as the Ising model hereafter for simplicity) and even
two-dimensional (2D) Ising model with non-zero external field to our knowledge.
Here by using an elementary but rigorous method, we obtain an exact solution to
the partition function of the Ising model with $N$ lattice sites. It is a sum
of $2^N$ exponential functions and holds for $D$-dimensional ($D=1,2,3,...$)
Ising model with or without the external field. This solution provides a new
insight into the problem of the Ising model and the related difficulties, and
new understanding of the classic exact solutions for one-dimensional (1D)
(Kramers and Wannier, 1941) or 2D Ising model (Onsager, 1944). With this
solution, the specific heat and magnetisation of a simple 3D Ising model are
calculated, which are consistent with the results from experiments and/or
numerical simulations. Furthermore, the solution here and the related
approaches, can also be available to other models like the percolation and/or
the Potts model.
