Consider the following Hamiltonian:

$$ H=-\sum_{i\neq j}J_{ij}S_iS_j-\sum_i H_iS_i $$

where $S_i\in\{-1,1\}$, and the summed pair $i,j$ can be any two distinct indices (not necessary adjacent spins). If we were to find the ground state of the system, would frustration be a good measure of the hardness of the problem? And if so, is there any way to quantify the frustration for this system?


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