Ising model open chain and periodic boundary conditions

[LagrangeEuler]

One dimensional Ising model is often treated as open chain system with free ends. Then when external field is added it is treated with cyclic boundary condition. Can someone explain me are those methods equivalent, or not?

 

[Jarek 31]

The main reason is probably computational cost of quantum treatment of transverse-filed Ising model, naively growing exponentially with the number of spins.

However, classical transverse field Ising model for infinite 1D lattice can be well approximated with MERW ( https://en.wikipedia.org/wiki/Maximal_entropy_random_walk ).
Also, 2D classical Ising for finite width approximation: "w x infinity" lattice e.g. with cyclic boundary conditions can be solved analytically with MERW - for both see https://arxiv.org/pdf/1912.13300