  A consistent theory of the ground state energy and its splitting due to the
process of tunneling for the Lipkin model is presented. For the functional
integral in terms of the spin coherent states for the partition function of the
model we accurately calculate the trivial and the instanton saddle point
contributions. We show that such calculation has to be perfomed very accurately
taking into account the discrete nature of the functional integral. Such
accurate consideration leads to finite corrections to a naive continous
consideration. We present comparison with numerical calculation of the ground
state energy and the tunneling splitting and with the results obtained by the
quasiclassical method and get excellent agreement.
