  In this paper, the frustration properties of the Ising model on a
one-dimensional monoatomic equidistant lattice in an external magnetic field
are investigated, taking into account the exchange interactions of atomic spins
at the sites of the first, second, and third neighbors. Exact analytical
expressions for the thermodynamic functions of the system are obtained by the
Kramers--Wannier transfer-matrix method. A magnetic phase diagram of the ground
state of such a spin system is constructed and studied thoroughly. The points
and lines of frustrations of the system depending on the values and signs of
exchange interactions and on an external magnetic field are found. The criteria
for the occurrence of magnetic frustrations in the presence of competition
between the energies of exchange interactions and an external magnetic field
are formulated. The peculiar features are investigated and the values of
entropy and magnetization of the ground state of this model are obtained in the
frustration regime and beyond it. Various types of behavior of entropy,
magnetization, and magnetic susceptibility depending on the model parameters
are revealed.
