论文标题
与下一个邻居相互作用的群集模型的精确解决方案
Exact solution of a cluster model with next-nearest-neighbor interaction
论文作者
论文摘要
具有下一个最邻居相互作用和另外两个复合相互作用的一维聚类模型。获得自由能，并精确得出相关函数。该模型是通过自动从其相互作用自动获得的转换来对角线的，该转换是约旦 - 瓦格转换的代数概括。无间隙条件表示为立方方程的根部的条件，并准确地获得了相图。我们发现，该代数方程的根分布决定了远程顺序的存在，并且我们再次获得了地面相图。我们还得出了相应的保形场理论的中心电荷。最后，我们注意到，我们的结果对于无限数量的可解决的旋转链的相互作用遵守相同的代数关系是普遍有效的。
A one-dimensional cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a transformation obtained automatically from its interactions, which is an algebraic generalization of the Jordan-Wigner transformation. The gapless condition is expressed as a condition on the roots of a cubic equation, and the phase diagram is obtained exactly. We find that the distribution of roots for this algebraic equation determines the existence of long-range order, and we again obtain the ground-state phase diagram. We also derive the central charges of the corresponding conformal field theory. Finally, we note that our results are universally valid for an infinite number of solvable spin chains whose interactions obey the same algebraic relations.
