Onsager reaction field theory applied to the phase diagram of Heisenberg chain with ferromagnetic long-range interaction and antiferromagnetic nearest-neighbor interaction

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) (J) over tilde. The ferromagnetic long-range interactions considered in this paper decay as J/r(p) with the distance r between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of alpha = (J) over tilde /J and p. At finite temperatures and in the region alpha < alpha(c)(p) in which alpha(c)(p) is dependent of p, the ferromagnetic-paramagnetic phase transition survives for 1 < p < 2 and no phase transition exists for p >= 2. At alpha = alpha(c)(p), the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for p > 1. The ground state of the system keeps ferromagnetic when alpha < alpha(c)(p). But for alpha > alpha(c), the system becomes antiferromagnetic at all temperatures.