Gibbs fields with continuous spins are studied, the underlying graphs of which can be of unbounded vertex degree and the spin–spin pair interaction potentials are random and unbounded. A high-temperature uniqueness of such fields is proved to hold under the following conditions: (a) the vertex degree is of tempered growth, i.e., controlled in a certain way; (b) the interaction potentials $$W_{xy}$$ W xy are such that $$\Vert W_{xy}\Vert =\sup _{\sigma ,\sigma '} |W_{xy}(\sigma , \sigma ')|$$ ‖ W xy ‖ = sup σ , σ ′ | W xy ( σ , σ ′ ) | are independent (for different edges $$\langle x, y \rangle $$ ⟨ x , y ⟩ ), identically distributed and exponentially integrable random variables.

中文翻译：

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无界度图上具有无界随机相互作用的吉布斯场的唯一性

研究了具有连续自旋的吉布斯场，其基础图可以是无界顶点度并且自旋-自旋对相互作用势是随机和无界的。这些场的高温唯一性被证明在以下条件下成立： (a) 顶点度是缓和增长的，即以某种方式控制；(b) 相互作用势 $$W_{xy}$$W xy 使得 $$\Vert W_{xy}\Vert =\sup _{\sigma ,\sigma '} |W_{xy}(\sigma , \sigma ')|$$ ‖ W xy ‖ = sup σ , σ ′ | W xy ( σ , σ ′ ) | 是独立的（对于不同的边 $$\langle x, y \rangle $$ ⟨ x , y ⟩ ），同分布且指数可积分的随机变量。