In the study of Ising spin glass models, Barahona investigates the computational complexity of two key problems: computing the magnetic partition function and finding a ground state. For a finite two-dimensional lattice, these problems can be solved using algorithms that require a number of steps polynomial in the size of the lattice. However, in both two-dimensional and three-dimensional cases, these problems are proven to be NP-hard, indicating that it is highly unlikely to find a polynomial-time algorithm to solve them.In the study of Ising spin glass models, Barahona investigates the computational complexity of two key problems: computing the magnetic partition function and finding a ground state. For a finite two-dimensional lattice, these problems can be solved using algorithms that require a number of steps polynomial in the size of the lattice. However, in both two-dimensional and three-dimensional cases, these problems are proven to be NP-hard, indicating that it is highly unlikely to find a polynomial-time algorithm to solve them.