  For arbitrary Ising-like models of any dimension and Hamiltonians with a
finite support with all possible multispin interactions and boundary conditions
with a shift, the exact value of the free energy in the thermodynamic limit is
obtained at some parametrically specified set of multispin interaction
coefficients. In this case, half of the multispin interaction coefficients and
the coordinates of the special eigenvector corresponding to the largest
eigenvalue of the elementary transfer matrix are parameters, and the second
half of the multispin coefficients is calculated using simple explicit
formulas. For models with Hamiltonians invariant under the reversal of signs of
all spins, the formulas are simplified. As examples of independent interest,
solutions are written for the cases when the support of the Hamiltonian is a
simplex, a cube, the support of the ANNNI model in spaces of 2, 3 and arbitrary
dimensions.
