Systems featuring hard-core–soft-shell repulsive pair potentials can form ordered phases, where particles organize themselves in aggregates with nontrivial geometries. The dimer crystal formed by one such potential, namely, the hard-core plus generalized exponential model of order 4, has been recently investigated, revealing a low-temperature structural phase transition, with the onset of nematic ordering of the dimers. In the present work, we aim to characterize this phase transition via a mean-field theory, by which a detailed analysis of the low-temperature properties of the system is carried out under quadrupole approximation. We determine the transition temperature and identify its order parameter, highlighting the link between the structural transition and the nematic ordering of the system. The first-order character of the transition is established and supported by the Landau expansion of the free energy in powers of the order parameter. The theory is subsequently generalized to take into account lattice vibrations and dimer length fluctuations. Finally, we provide an explanation for the anomalous behavior displayed by the specific heat in the vanishing-temperature limit, which is also supported by Monte Carlo simulations.

中文翻译：

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核心软化颗粒二维二聚体晶体中的结构转变、取向顺序和反常比热

具有硬核-软壳排斥对势的系统可以形成有序相，其中粒子以非平凡几何形状的聚集体组织起来。最近研究了由这样一种势形成的二聚体晶体，即 4 阶硬核加广义指数模型，揭示了伴随二聚体向列有序开始的低温结构相变。在目前的工作中，我们的目标是通过平均场理论来表征这种相变，通过四极近似对系统的低温特性进行详细分析。我们确定了转变温度并确定了其有序参数，突出了结构转变与系统向列有序之间的联系。跃迁的一阶特征是由自由能的阶次参数幂的朗道展开建立和支持的。该理论随后被推广以考虑晶格振动和二聚体长度波动。最后，我们对消失温度极限内的比热表现出的异常行为进行了解释，这也得到了蒙特卡罗模拟的支持。