Periodic Striped Ground States in Ising Models with Competing Interactions
Periodic Striped Ground States in Ising Models with Competing Interactions
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DOI：
10.1007/s00220-016-2665-0
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发表时间：
2016-11-01
影响因子：
2.4
通讯作者：
Seiringer, Robert
中科院分区：
文献类型：
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作者：
Giuliani, Alessandro;Seiringer, Robert
我们考虑了具有短程铁磁和长程铁磁、幂衰减、反铁磁相互作用的二维和三维伊辛模型。我们设J为铁磁与反铁磁相互作用强度之比。这两种相互作用之间的竞争导致系统在正旋背景下形成负自旋的区域，反之亦然。如果长程相互作用的衰变指数p大于d+1，其中d为空间维度，则所有小于某一临界值J(C)(P)的J值都会发生这种情况，超过该临界值，基态是均匀的。本文给出了系统在J(C)(P)的左邻域中p>；2d和J的无限体积基态的特征。特别地，我们证明了由无限条(d=2)或板条(d=3)组成的、具有相同最佳宽度和取向、交变磁化强度的准一维态是无限体积基态。我们的证明是基于局域界和反射正性相结合的。
We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J(c)(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J(c)(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.