We analyze the phase diagram of an elementary statistical lattice model of classical, discrete, spin variables, with nearest-neighbor ferromagnetic isotropic interactions in competition with chiral interactions along an axis. At the mean-field level, we show the existence of critical lines of transition to a region of modulated (helimagnetic) structures. We then turn to the analysis of the analogous problem on a Cayley tree. Taking into account the simplicity introduced by the infinite-coordination limit of the tree, we explore several details of the phase diagrams in terms of temperature and a parameter of competition. In particular, we characterize sequences of modulated (helical) structures associated with devil’s staircases of a fractal character.

我们分析了经典、离散、自旋变量的基本统计晶格模型的相图，其中最近邻铁磁各向同性相互作用与沿轴的手性相互作用竞争。在平均场水平，我们展示了过渡到调制（螺旋磁）结构区域的临界线的存在。然后我们转向分析凯莱树上的类似问题。考虑到树的无限协调极限引入的简单性，我们在温度和竞争参数方面探索了相图的几个细节。特别是，我们描述了与分形特征的魔鬼楼梯相关的调制（螺旋）结构序列。