Re-entrant Disordered Phase in a System of Repulsive Rods on a Bethe-like Lattice

Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice

We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods. The Bethe lattice, which is conventionally used to derive the self-consistent equations in the Bethe approximation, is not suitable for studying the hard-rods system, as it does not allow a dense packing of rods. We define a new lattice, called the random locally tree-like layered lattice, which allows a dense packing of rods, and for which the approximatio…

Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations

The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SAARs) model, the surface is represented by a twodimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Pe…

Bethe格上扩展哈伯德模型在原子极限下的精确解

Exact solution of the extended Hubbard model in the atomic limit on the Bethe Lattice

我们研究了在有限温度下费米粒子系统的Bethe晶格与协调数z和现场U和最近邻V相互作用的网站上的相图。这是扩展的哈伯德模型在原子极限下的物理实现。利用运动方程法对模型进行了精确求解。对于一个有吸引力的intersite势，我们发现，在半填充，一个相变向破缺的粒子-空穴对称状态。临界温度，作为相关参数的函数，具有重入的行为，已经观察到的等效自旋1伊辛模型的贝特晶格。

Husimi晶格上的硬刚性棒

Hard rigid rods on Husimi lattices

本文研究正方形和三角形 Husimi 晶格上硬刚性棒的热力学行为，发现 $k\ge4$ 时出现各向同性-向列相变，并分析了临界参数及完全填充熵，结果比 Bethe 晶格更接近二维晶格。

Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit

Although hard rigid rods ($k$-mers) defined on the square lattice have been widely studied in the literature, their entropy per site, $s(k)$, in the full-packing limit is only known exactly for dimers ($k=2$) and numerically for trimers ($k=3$). Here, we investigate this entropy for rods with $k \le 7$, by defining and solving them on Husimi lattices built with diagonal and regular square lattice clusters of effective lateral size $L$, where $L$ defines the level of approximation to the square lattice. Due to an $L$-parity effect, by increasing $L$ we obtain two systematic sequences of values …

Sequence of phase transitions in a model of interacting rods

In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $κ=\ell/a$ and the temperature are varied. There are essentially two classes of transitions. One corresponds to the Ising-type spontaneous symmetry breaking transition and the second belongs to less-studied phase transitions of geometrical origin. The latter class of transitions appear at fixed values of $κ$ irrespective of the temperature, whereas the critical coupling for the spontaneous symmetry break…