Modulation of Local Magnetization in two-dimensional   Axial-Next-Nearest-Neighbor Ising model
  The axial next-nearest-neighbor Ising model is studied in two dimensions at finite temperature using the density matrix renormalization group. The model exhibits phase transition of the second-order between the antiphase in low temperature and the modulated phase in high temperature. Observing the domain wall free energy, we confirm that the modulation period in high-temperature side is well explained by the free-fermion picture. 
Rene Derian, Andrej Gendiar, and Tomotoshi Nishino