In a one-dimensional system of N spins, the allowed values of each spin are σ1 = {1,2,3,...,q}, where q ≥ 2 is an integer. The energy of the system is
\(-J \sum_{i=1}^N \delta_{\sigma_i, \sigma_{i+1}}\)
where J > 0 is a constant. If periodic boundary conditions are imposed, the number of ground states of the system is
1
q
2
Nq
3
qN
4
1