Abstract

The Ising model on an one-dimensional monoatomic equidistant lattice with different exchange interactions between atomic spins at the sites of nearest neighbors and different interactions between atomic spins at the sites of second neighbors is investigated. The generalized Kramers–Wannier transfer matrix with translation on two periods of a lattice is derived. The phase diagrams representing all possible magnetic types of ordering in the ground state are constructed. Many triple points of intersection of phases and lines of pair coexistence of phases in strict accordance with the Gibbs phase rule are found and a property similar to supercooling and superheating is detected. It is shown that at triple points the phases are not individualized but significantly frustrated, which corresponds to the phenomenon of critical opalescence. Exact analytical expressions for the Gibbs free energy, as well as for such thermodynamic characteristics of the system as internal energy, heat capacity and entropy including zero-temperature entropy are derived. A variety of particular cases are analyzed and a comparison is made with all known results including on a two-dimensional lattice.

中文翻译：

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磁场不存在的广义伊辛模型

摘要

研究了一维单原子等距晶格上的伊辛模型，该晶格具有最近邻位置处的原子自旋之间具有不同的交换相互作用而第二邻域位置处的原子自旋之间具有不同的相互作用。推导了在两个晶格周期上平移的广义Kramers-Wannier传递矩阵。构造了表示基态中所有可能的磁性排序的相图。严格按照吉布斯（Gibbs）相规则，发现了许多相交线和相对线共存的三重点，并且检测到类似于过冷和过热的性质。结果表明，在三相点处，相没有被个体化而是被严重挫败，这与临界乳光现象相对应。得出了吉布斯自由能以及系统的热力学特性（如内部能量，热容量和包括零温度熵的熵）的精确解析表达式。分析了各种特殊情况，并与所有已知结果进行了比较，包括二维晶格。