Cayley树上具有不可数自旋值集模型的Gibbs测度的唯一性
Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree
摘要：
我们考虑具有最近邻相互作用和自旋值集$[0,1]$的模型，在$k\geq 1$阶Cayley树上。已知模型的“分裂吉布斯测度”可以用一个非线性积分方程的解来描述。对于任意的$k\geq 2$，我们找到了一个充分条件，在这个条件下，积分方程有唯一解，从而相应的模型有唯一的分裂Gibbs测度.
英文摘要：
We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary $k\geq 2$ we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.
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