Abstract
The Ising model is a well known statistical model which can be solved exactly by various methods. The most familiar one is the transfer matrix method. Sometimes it can be difficult to approach the open boundary case rather than periodic boundary ones in higher dimensions. But physically it is more intuitive to study the open boundary case, as it gives a closer view of the real system. We have introduced a new method called the pairing method to determine the exact partition function for the simplest case, a 1D Ising lattice. This method simplifies the problem's complexities and reduces it to a pure combinatorial problem. The study also reveals that it is possible to apply this pairing method in the case of a 2D square lattice. The obtained results agree perfectly with the values in the literature and this new approach provides an algorithmic insight to deal with such problems.
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