It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two Majorana zero modes at the two ends of the chain in "Majorana language".
It is evident that the ground states of an infinite (without ends) 1D Ising chain are degenerate. How can I understand the degeneracy in its Majorana counterparts which is also infinite (without ends)?
Another question which confuses me is whether we can treat this two-fold degeneracy as two Majorana zero modes in 1D Ising model. If not, what is the relationship between the two-fold degeneracy in the Ising model and the two Majorana zero modes in the free Majorana model?