  We studied the phase transitions and magnetic properties of the Ising model
on a square lattice by the replica Monte Carlo method and by the method of
transfer-matrix, the maximum eigenvalue of which was found by Lanczos method.
The competing exchange interactions between nearest neighbors $J_{1}$, second
$J_{2}$, third neighbors $J_{3}$ and an external magnetic field were taken into
account. We found the frustration points and expressions for the frustration
fields, at crossing of which cardinal changes of magnetic structures
(translational invariance changes discontinuously) take place. A comparative
analysis with 1D Ising model was performed and it was shown that the behavior
of magnetic properties of the 1D model and the 2D model with $J_{1}$ and
$J_{3}$ interactions reveals detailed similarity only distinguishing in scales
of magnetic field and temperature.
