Phase transition of nematic phase exposed to a uniaxial field is studied in the Behte approximation. The transition is of first order, and a jump at the transition decreases as the field is increased. At length a critical point appears at a critical field, beyond which no transition occurs. The critical point is especially of interest, where an estimated value of the critical field derived here is smaller than a half of an approximate value of mean field theory. Calculus of a free energy, which is inevitable for an analysis of first order phase transition, is discussed. The specific heat diverges with an index 2/3 at the critical field as temperature changes, which is elucidated to be a general character of the critical point without symmetry change at every classical theory.