A One-Dimensional Statistical Mechanics Model with Exact Transfer Integral Solution

n |sn−sn+1|, is presented. This Ising-like model is an interesting example of a graduate-level statistical mechanics problem where the eigenfunctions and eigenvalues of an integral operator, the transfer integral, can be determined exactly. This can be contrasted with the determination of eigenfunctions and eigenvalues of differential operators, such as the quantum mechanical finite-depth square well. In this problem transcendental equations leading to the eigenvalues and eigenfunctions are also obtained. The largest eigenvalue is identified and the free energy is determined. The thermodynamic properties depend on the sign of J , unlike classical Ising or Heisenberg models.