We investigate the application of the line-graph operator to one-dimensional spin models with periodic boundary conditions. The spins (or interactions) in the original spin structure become the interactions (or spins) in the resulting spin structure. We identify conditions which ensure that each new spin structure is stable, that is, its spin configuration minimizes its internal energy. Then, making a correspondence between spin configurations and binary sequences, we propose a model of information growth and evolution based on the line-graph operator. Since this operator can generate frustrations in newly formed spin chains, in the proposed model such frustrations are immediately removed. Also, in some cases, the previously frustrated chains are allowed to recombine into new stable chains. As a result, we obtain a population of spin chains whose dynamics is studied using Monte Carlo simulations. Lastly, we discuss potential applications to areas of research such as combinatorics and theoretical biology.

我们研究了线图算子在具有周期性边界条件的一维自旋模型中的应用。原始自旋结构中的自旋（或相互作用）变成了所得自旋结构中的相互作用（或自旋）。我们确定了确保每个新自旋结构稳定的条件，即其自旋配置使其内能最小化。然后，在自旋配置和二进制序列之间进行对应，我们提出了基于线图算子的信息增长和演化模型。由于这个算子可以在新形成的自旋链中产生挫折，在所提出的模型中，这种挫折会立即被消除。此外，在某些情况下，允许先前受挫的链重新组合成新的稳定链。因此，我们获得了一群自旋链，其动力学使用蒙特卡罗模拟进行研究。最后，我们讨论了在组合学和理论生物学等研究领域的潜在应用。