Ising Model on periodic and quasi-periodic chains in presence of magnetic field: some exact results

We present a general procedure for calculating the exact partition function of an Ising model on a periodic chain in presence of magnetic field considering both open and closed boundary conditions. Using same procedure on a quasiperiodic (Fibonacci) chain we have established a recurrence relation among partition functions of different Fibonacci generations from n-th to (n+6)-th. In the large N limit we find $(2\tau +1)F_{n+1}=F_{n+2}$; where $\tau$ is the golden mean and $F_n$ stands for free energy/spin for the n-th generation. We have also studied chemical potential in both cases.