论文标题
相互作用杆模型中的相变的顺序
Sequence of phase transitions in a model of interacting rods
论文作者
论文摘要
在相互作用的二维晶格间距$ a $ $ 2 \ ell $ $ 2 \ ell $的薄刚性杆的系统中，我们表明，由于耦合强度$κ= \ ell/a $，并且温度有多种相变。本质上有两类的过渡。一个对应于Ising型自发对称性断裂过渡，第二个属于几何起源的研究相变。后者的过渡类别以$κ$的固定值出现，而不论温度如何，而自发对称性断裂过渡的临界耦合取决于它。通过改变温度，相位边界可能会相互交叉，从而导致具有无限多相的丰富相行为。我们的结果基于方形晶格上的蒙特卡洛模拟，以及对伯特晶格上功能流程方程的固定分析。
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 breaking transition depends on it. By varying the temperature, the phase boundaries may cross each other, leading to a rich phase behaviour with infinitely many phases. Our results are based on Monte Carlo simulations on the square lattice, and a fixed-point analysis of a functional flow equation on a Bethe lattice.
