Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) J̃. The ferromagnetic long-range interactions considered in this paper decay as J/rp 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 α = J̃/J and p. At finite temperatures and in the region α < αc(p) in which αc(p) is dependent of p, the ferromagnetic-paramagnetic phase transition survives for 1 < p < 2 and no phase transition exists for p ≥ 2. At α = αc(p), the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for p > 1. The ground state of the system keeps ferromagnetic when α < αc(p). But for α > αc, the system becomes antiferromagnetic at all temperatures.

中文翻译：

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昂萨格反应场理论应用于具有铁磁长程相互作用和反铁磁最近邻相互作用的海森堡链相图

Onsager反应场理论用于研究具有反铁磁最近邻相互作用（NNI）的一维铁磁长程相互作用自旋链Ĵ̃. 本文考虑的铁磁长程相互作用衰减为Ĵ/rp随着距离r格点之间。发现系统的零温度和有限温度相图都受到铁磁长程和反铁磁NNI之间相互作用的强烈影响。临界温度和均匀磁化率是作为函数的α = Ĵ̃/Ĵ和p. 在有限的温度和区域内α < αC(p)其中αC(p)依赖于p，铁磁 - 顺磁相变存在1 < p < 2并且不存在相变p ≥ 2. 在α = αC(p)，铁磁 - 反铁磁相变发生在零温度下p > 1. 当系统基态保持铁磁性时α < αC(p). 但对于α > αC，系统在所有温度下都变成反铁磁性的。