论文标题
吉布斯在凯利树上具有混合旋转1和自旋1/2的Ising模型的测量
Gibbs measures of the Ising model with mixed spin-1 and spin-1/2 on a Cayley tree
论文作者
论文摘要
在本文中，在二阶Cayley树上考虑了具有混合自旋（1,1/2）的ISING模型。分裂吉布斯度量的构造给出了模型，该模型允许建立相变的存在（Gibbs测量的非唯一性）。我们指出，在相变的区域中，考虑的模型在铁磁和抗铁磁方案中具有三种翻译不变的吉布斯度量，而经典的伊辛模型在抗嗜血杆菌方面不具有此类吉布斯度量。事实证明，像Ising模型一样，所考虑的模型表现出无序的吉布斯度量。因此，通过树指数的马尔可夫链研究了这种无序吉布斯措施的非肢体性和极端性。
In the present paper, the Ising model with mixed spin-(1,1/2) is considered on the second order Cayley tree. A construction of splitting Gibbs measures corresponding the model is given which allows to establish the existence of the phase transition (non-uniqueness of Gibbs measures). We point out that, in the phase transition region, the considered model has three translation-invariant Gibbs measures in the ferromagnetic and anti-ferromagnetic regimes, while the classical Ising model does not possesses such Gibbs measures in the anti-ferromagnetic regime. It turns out that the considered model, like the Ising model, exhibits a disordered Gibbs measure. Therefore, non-extremity and extremity of such disordered Gibbs measures is investigated by means of tree-indexed Markov chains.
