竞争相互作用系统中的调制和关联长度
Modulation and correlations lengths in systems with competing interactions
摘要：
我们研究关联函数中存在的竞争的长期和短期的相互作用，找到多个相关和调制长度。本文计算了任意长程相互作用下伊辛铁磁体的基态条宽。在大的$n$系统中，我们证明了对于一个被一般的竞争长程相互作用挫败的短程系统，交叉温度$T^*$转向未挫败短程系统的临界温度（即，其中消除了令人沮丧的长距离相互作用）。我们还表明，除了某些特殊的交叉点，相关和调制长度的总数仍然保守。我们推导出一个一般系统的调制长度随温度的变化与铁磁相互作用和相反的长程相互作用的基态附近的表达式。我们说明，与确切的偶极相互作用的关联函数有很大的不同，其中的偶极之间的标量积的形式被假定。
英文摘要：
We examine correlation functions in the presence of competing long and short ranged interactions to find multiple correlation and modulation lengths. We calculate the ground state stripe width of an Ising ferromagnet, frustrated by an arbitrary long range interaction. In large $n$ systems, we demonstrate that for a short range system frustrated by a general competing long range interaction, the crossover temperature $T^*$ veers towards the critical temperature of the unfrustrated short range system (i.e., that in which the frustrating long range interaction is removed). We also show that apart from certain special crossover points, the total number of correlation and modulation lengths remains conserved. We derive an expression for the change in modulation length with temperature for a general system near the ground state with a ferromagnetic interaction and an opposing long range interaction. We illustrate that the correlation functions associated with the exact dipolar interactions differ substantially from those in which a scalar product form between the dipoles is assumed.
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