INTERACTING-FERMION APPROXIMATION IN THE 2-DIMENSIONAL AXIAL NEXT-NEAREST-NEIGHBOR ISING-MODEL

We investigate the effect of including domain-wall interactions in the two-dimensional axial next-nearest-neighbor Ising model. At low temperatures this problem is reduced to a one-dimensional system of interacting fermions which can be treated exactly. It is found that the critical boundaries of the low-temperature phases are in good agreement with those obtained using a free-fermion approximation. In contrast with the monotonic behavior derived from the free-fermion approach, the wall density or wave number displays reentrant phenomena when the ratio of the next-nearest-neighbor and nearest-neighbor interactions is greater than 1/2.