论文标题
随机键模模型及其在双曲空间中的双重模型
The Random-Bond Ising Model and its dual in Hyperbolic Spaces
论文作者
论文摘要
我们使用Monte Carlo和高温序列膨胀技术分析了随机键模模型（RBIM）在封闭双曲线表面上的热力学特性。我们还分析了双rbim，这是一个模型，在没有疾病的情况下，通过Kramers-Wannier二元性与RBIM有关。即使在自偶型晶格上，该模型也与RBIM不同，与欧几里得案不同。我们通过对Kramers的仔细重新衍生 - 强烈的双重性来解释这一异常。对于（双 - ）RBIM，我们计算Paramagnet-to-Ferromagnet相变为温度$ t $的函数，以及抗铁磁债券的比例$ p $。我们发现，随着RBIM温度的降低，Paramagnet通过二阶过渡与平均场行为兼容的二阶过渡相位。相反，在没有障碍和沿Nishimori线的情况下，双rbim都经历了从帕拉格内特到铁磁铁的强烈一阶过渡。我们研究了两种过渡的多种双曲线镶嵌，并评论了协调数和曲率的作用。双rbim中铁磁相的程度对应于独立的比特和相叉噪声下双曲线表面代码的可更正阶段。
We analyze the thermodynamic properties of the random-bond Ising model (RBIM) on closed hyperbolic surfaces using Monte Carlo and high-temperature series expansion techniques. We also analyze the dual-RBIM, that is the model that in the absence of disorder is related to the RBIM via the Kramers-Wannier duality. Even on self-dual lattices this model is different from the RBIM, unlike in the euclidean case. We explain this anomaly by a careful re-derivation of the Kramers--Wannier duality. For the (dual-)RBIM, we compute the paramagnet-to-ferromagnet phase transition as a function of both temperature $T$ and the fraction of antiferromagnetic bonds $p$. We find that as temperature is decreased in the RBIM, the paramagnet gives way to either a ferromagnet or a spin-glass phase via a second-order transition compatible with mean-field behavior. In contrast, the dual-RBIM undergoes a strongly first order transition from the paramagnet to the ferromagnet both in the absence of disorder and along the Nishimori line. We study both transitions for a variety of hyperbolic tessellations and comment on the role of coordination number and curvature. The extent of the ferromagnetic phase in the dual-RBIM corresponds to the correctable phase of hyperbolic surface codes under independent bit- and phase-flip noise.
