  The Lenz-Ising-Onsager (LIO) problem in an external magnetic field in the
second quantization representation is the subject of consideration of the
paper. It is shown that the operator $V_h$ in the second quantization
representation corresponding to Ising spins interaction with the external
magnetic field $H$ can be represented in terms of single-subscript creation and
anihilation Fermi operators in such a form that the operator $V_h$ commutes
with the operator $\hat{P}\equiv(-1)^{\hat{S}}$, where $\hat{S}=
\sum_m\beta^{\dag}_m\beta_m$ is the operator of a total number of Fermions. The
possible consequences of such representation with it's relation to the LIO is
discussed. In particular, the constructive proof of the Lee-Yang theorem on the
absence of phase transition for Ising model in nonzero magnetic field $(\Re
h\neq 0)$ is demonstrated.

Statistical Mechanics