双曲格上依赖于边界条件的普适类
Boundary Condition dependent Universality Classes on a Hyperbolic Lattice
- Saha Institute of Nuclear Physics（萨哈核物理研究所）
- Homi Bhabha National Institute（霍米·巴巴国立研究所）
- University of Southampton（南安普顿大学）
- QuNu Labs Pvt. Ltd.（QuNu实验室私人有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究双曲格上Ising模型在不同边界条件下的临界行为，发现开放边界导致新的普适类，而有线边界符合平均场指数，强调边界条件对临界现象的关键影响。
AI中文摘要：
我们研究了具有开放和有线边界条件的欧几里得AdS$_2$的有限双曲镶嵌上的铁磁Ising模型。由于随着晶格的增长，有限比例的旋转仍保留在边界上，这些条件选择了不同的热力学行为。在{5,4}镶嵌中，使用高效虫算法在开放边界（OBC）上的蒙特卡洛模拟在$\beta_c J=0.632(3)$附近产生转变，磁化率数据在总自旋数$N$的缩放下塌缩。拟合的有限尺寸指数$1/\bar{\nu} \simeq 0.162$和$\gamma/\bar{\nu} \simeq 0.743$与平均场体积缩放有显著差异。有线边界（WBC）关联边界自旋，反而在$\beta_c J=0.348(4)$附近显示出与平均场指数一致的有序相转变。虽然WBC的平均场临界性与先前研究以及独立边界波动的抑制一致，但OBC指数暗示存在新的普适类。其他镶嵌的结果支持OBC观察到的缩放的稳健性。我们讨论了在不同边界条件之间插值的可能途径。我们的发现表明，在表征双曲格上的临界行为时，必须指定边界动力学。
英文摘要：
We study the ferromagnetic Ising model on finite hyperbolic tessellations of Euclidean AdS$_2$ with open and wired boundary conditions. Because a finite fraction of spins remains at the boundary as the lattice grows, these conditions select distinct thermodynamic behaviours. In the $\{5,4\}$ tessellation, Monte-Carlo simulations using efficient worm algorithms on open boundaries (OBC) yield a transition near $β_c J=0.632(3)$, with susceptibility data collapsing under scaling by the total number of spins $N$. The fitted finite-size exponents, $1/\barν \simeq 0.162$ and $γ/\barν \simeq 0.743$, differ substantially from the mean-field volume scaling. Wired boundaries (WBC), which correlate boundary spins, instead show a transition around $β_c J=0.348(4)$ to an ordered phase consistent with the mean-field exponents. While the mean-field criticality with WBC is consistent with previous studies and with the suppression of independent boundary fluctuations, the OBC exponents hint at the presence of a new universality class. Results from other tessellations support the robustness of the observed scaling with OBC. We discuss a possible route to interpolate between the different boundary conditions. Our findings show that boundary dynamics must be specified when characterizing critical behaviour on hyperbolic lattices.
