The work is devoted to gradient Gibbs measures (GGMs) of an SOS model with countable set $\mathbb{Z}$ of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbour gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several q-height-periodic translations invariant GGMs for q = 2, 3, 4.

中文翻译：

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凯莱树上交变磁力 SOS 模型的梯度吉布斯测量

这项工作致力于具有可数集的 SOS 模型的梯度吉布斯测度 (GGM) $\mathbb{Z}$凯莱树上的自旋值和交变磁性。该模型由最近邻梯度相互作用势定义。使用 Külske-Schriever 论证，基于边界法方程，我们给出了q = 2, 3, 4 的几个q高度周期平移不变 GGM 。