AI 中文总结
本文研究蜂窝晶格阻挫J₁-J₂伊辛模型，引入复值向列序参量区分相态，揭示比热峰与边界条件、长宽比的关联，对J₂=-0.5和J₂=-1无法明确区分相变类型，还得到J₂=-1/4时的基态熵渐近估计值。
AI 中文摘要
我们研究蜂窝晶格上的阻挫J₁-J₂伊辛模型，其中铁磁近邻耦合固定为J₁=1，反铁磁次近邻相互作用较强，即J₂≤-1/4。对于该J₂取值范围，人们知之甚少；而当J₂的负值较小时，系统在低温下呈铁磁有序，且似乎仍处于伊辛普适类。此前研究表明该模型具有高度简并的基态，且推测存在某种相变。我们引入复值向列序参量，可区分高温顺磁相与低温下观测到的部分无序条纹相。该相中的构型由沿一个晶格方向平行的自旋条纹构成，这些条纹整体沿其余两个方向蜿蜒，形成部分无序的基态。早期研究中观测到的比热尖锐峰仅在使用周期性边界条件时出现，自由边界条件下则不存在。此外，我们揭示了该行为对所研究样品的长宽比存在显著依赖。最终，即使对J₂=-0.5和J₂=-1进行细致的有限尺寸标度分析，也无法明确区分无任何奇异性的交叉行为与某种连续相变，包括无限阶Berezinskii-Kosterlitz-Thouless（BKT）型相变的可能性。对于J₂=-1/4，我们发现系统在所有温度下均保持无序，且呈现有限的每格点基态熵，我们的模拟给出热力学极限N→∞下的精确渐近估计值为S(T=0)/N=0.23096093(14)。
英文摘要
We study the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at $J_1=1$ and strong antiferromagnetic next-nearest-neighbor interactions, i.e., $J_2 \leq -1/4$. Little is known for this range of $J_2$, whereas for less negative values of $J_2$ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for $J_2 = -0.5$ and $J_2 = -1$ is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For $J_2=-1/4$ we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate $S(T=0)/N = 0.230\,960\,93(14)$ in the thermodynamic limit $N\rightarrow\infty$.
Comments25 pages, 21 figures, 3 tables
