二维晶格模型中团簇和条纹的周期有序性。I.基态、平均场phase diagram和无序相的结构
Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases
摘要：
纳米粒子或大分子之间的短程吸引和长程排斥（SALR）可以导致在固体表面、流体界面或膜上自发形成斑图形成。为了研究这类系统的自组装，我们考虑了一个具有最近邻吸引和第三邻排斥的三角格子模型。在模型的基态（$T=0$），对于小的化学势值$μ$，晶格是空的，而对于大的$μ$，晶格被完全占据。对于中间值的$μ$周期性分布的集群，气泡或条纹出现，如果斥力足够强。在真空相和有序团簇相以及团簇相和片层（条纹）相共存时，单位点熵不为零。由于这种基态简并，由团簇或条纹组成的无序流体相是稳定的，并且表面张力消失。对于$T>0$，我们在平均场近似下构造了相图，并在自洽的Brazovskii型场论中计算了关联函数。
英文摘要：
The short-range attraction and long-range repulsion (SALR) between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbour attraction and third-neighbour repulsion. At the ground state of the model ($T=0$) the lattice is empty for small values of the chemical potential $μ$, and fully occupied for large $μ$. For intermediate values of $μ$ periodically distributed clusters, bubbles or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For $T>0$ we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.
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