  We investigate whether the floating phase (where the correlation length is
infinite and the spin-spin correlation decays algebraically with distance)
exists in the temperature($T$) - frustration parameter ($\kappa$) phase diagram
of 2D ANNNI model. To identify this phase, we look for the region where (i)
finite size effect is prominent and (ii) some relevant physical quantity
changes somewhat sharply and this change becomes sharper as the system size
increases. For $\kappa < 0.5 $, the low temperature phase is ferromagnetic and
we study energy and magnetization. For $\kappa > 0.5 $, the low temperature
phase is antiphase and we study energy, layer magnetization, length of domain
walls running along the direction of frustration, number of domain-intercepts
that are of length 2 along the direction of frustration, and the number of
domain walls that do not touch the upper and/or lower boundary. In agreement
with some previous studies, our final conclusion is that, the floating phase
exists, if at all, only along a line.
