Floating Phase in 2D ANNNI Model

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.