  One-band Hubbard model with hopping parameter $t$ and Coulomb repulsion $U$
is considered at half filling. By means of the Schwinger bosons and slave
Fermions representation of the electron operators and integrating out the
spin-singlet Fermi fields an effective Heisenberg model with antiferromagnetic
exchange constant is obtained for vectors which identifies the local
orientation of the spin of the itinerant electrons. The amplitude of the spin
vectors is an effective spin of the itinerant electrons accounting for the fact
that some sites, in the ground state, are doubly occupied or empty. Accounting
adequately for the magnon-magnon interaction the N\'{e}el temperature is
calculated. When the ratio $\frac tU$ is small enough ($\frac tU\leq 0.09$) the
effective model describes a system of localized electrons. Increasing the ratio
increases the density of doubly occupied states which in turn decreases the
effective spin and N\'{e}el temperature. The phase diagram in plane of
temperature $\frac {T_N}{U}$ and parameter $\frac tU$ is presented. The quantum
critical point ($T_N=0$) is reached at $\frac tU=0.9$. The magnons in the
paramagnetic phase are studied and the contribution of the magnons'
fluctuations to the heat capacity is calculated. At N\'{e}el temperature the
heat capacity has a peak which is suppressed when the system approaches quantum
critical point.
