Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 209 / 3 / i / Solution

In the one-dimensional zero-field Ising model, the bond variables ${\tau }_j={\sigma }_j{\sigma }_{j+1}$ are independent andSince ${\sigma }_0{\sigma }_x={\prod }_{j=0}^{x-1}{\tau }_j$ for $x>0$,