  The frustration properties of the Ising model on a one-dimensional monoatomic
equidistant lattice are investigated taking into account the exchange
interactions of atomic spins at the sites of the first (nearest), second
(next-nearest) and third neighbors. The exact solution of the model was
obtained using the Kramers--Wannier transfer matrix method. The types of
magnetic ordering of the ground state of the model are determined, and a
magnetic phase diagram is constructed. Criteria are formulated for the
occurrence of magnetic frustrations in the presence of competition between the
energies of exchange interactions. Non-zero entropy values in the ground state
of the frustrated system were found.

Statistical Mechanics