发表机构
Comisión Nacional de Energía Atómica (CNEA); Instituto Sábato, Universidad Nacional de San Martín; Department of Mathematical Sciences, UTEP（阿根廷国家原子能委员会; 萨巴托研究所，圣马丁国立大学; 德州大学埃尔帕索分校数学科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
在自由边界双曲格上，Ising 模型存在两个温度尺度：磁化率峰对应较低转变，边界扰动揭示较高热力学转变，且有限尺寸标度需用代指数。
AI 中文摘要
在 $\{5,4\}$ 双曲格上，最外层代在所有系统尺寸下占据 73% 的格点，使得宏观平均严格依赖于边界。我们通过蒙特卡洛模拟研究该几何结构上具有自由边界的铁磁 Ising 模型，证明常规观测量不再能识别单一临界尺度。相反，有限格点由两个不同的温度尺度组织。磁化率最大值在 $T_{c2}=1.4782(15)J/k_{B}$ 处识别出较低的转变尺度，无需外推。然而，在该尺度下序参量分布缺乏常规的不动点。一个不同的赝临界尺度在 $T^{*}\simeq1.67(3)$ 处出现，位于边界敏感的中间相内，此处 Binder 累积量曲线交叉，有效指数与平均场临界性相容。在 $T_{c2}$ 和 $T^{*}$ 之间，内部将边界涨落放大为诱导序。此外，由于体积随深度指数增长，有限尺寸标度必须用代指数而非总格点数来表述。标度区间内缺乏渐近幂律收敛，通过独立观测量确认 $T^{*}$ 是有限尺寸交叉而非热力学不动点。最后，仅对最外层代施加相干场，我们恢复了 $T_{pt}=2.81(1)J/k_{B}$ 处的上热力学转变，证明其在适当的边界扰动下仍然可及。
英文摘要
On the $\{5,4\}$ hyperbolic lattice, the outermost generation holds 73\% of the sites at all system sizes, making macroscopic averages strictly boundary-dependent. We study the ferromagnetic Ising model on this geometry with free boundaries by Monte Carlo simulation, demonstrating that conventional observables cease to identify a single critical scale. Instead, the finite lattices are organized by two distinct temperature scales. The susceptibility maximum identifies the lower transition scale at $T_{c2}=1.4782(15)J/k_{B}$ without extrapolation. However, the order-parameter distribution lacks a conventional fixed point at this scale. A distinct pseudocritical scale emerges instead at $T^{*}\simeq1.67(3)$ inside the boundary-sensitive intermediate phase, where Binder cumulant curves cross and effective exponents are compatible with mean-field criticality. Between $T_{c2}$ and $T^{*}$, the interior amplifies boundary fluctuations into induced order. Furthermore, because the volume grows exponentially with depth, finite-size scaling must be formulated in the generation index rather than the total number of sites. The lack of asymptotic power-law convergence in the scaling stretch confirms through an independent observable that $T^{*}$ is a finite-size crossover rather than a thermodynamic fixed point. Finally, by applying a coherent field to the outermost generation alone, we recover the upper thermodynamic transition at $T_{pt}=2.81(1)J/k_{B}$, demonstrating that it remains accessible under an appropriate boundary perturbation.
Comments17 pages, 7 figures
