Curvature-induced frustration in the $XY$ model on hyperbolic surfaces

Thermodynamic curvature for a two-parameter spin model with frustration

Microscopic models of realistic thermodynamic systems usually involve a number of parameters, not all of equal macroscopic relevance. We examine a decorated $(1+3)$ Ising spin chain containing two microscopic parameters: a "stiff" $K$ mediating the long-range interactions, and a "sloppy" $J$ operating within local spin groups. $K$ dominates the macroscopic behavior, and varying $J$ has weak effect except in regions where $J$ brings about transitions between phases through its conditioning of the local spin groups with which $K$ interacts. We calculate the heat capacity $C_H$, the magnetic susc…

二维几何挫折：负曲率硬盘流体的理想化与实现

Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard Disc Fluid in Negative Curvature

我们研究了一个简单的硬盘流体没有长程相互作用的常负高斯曲率的二维空间，双曲平面。这种几何形状提供了一个自然的机制，全球晶体秩序是受挫，使我们能够构建一个易于处理的模型无序单分散硬盘。我们扩展自由区理论和维里膨胀到这个政权，推导出系统的状态方程，并比较其预测与模拟附近的均衡包装在弯曲的空间。此外，我们调查包装和动力学三重周期性，负弯曲的表面，着眼于真正的生物和聚合物系统。

Critical Phenomena in Hyperbolic Space

In this paper we study the critical behavior of an $N$-component $ϕ^{4}$-model in hyperbolic space, which serves as a model of uniform frustration. We find that this model exhibits a second-order phase transition with an unusual magnetization texture that results from the lack of global parallelism in hyperbolic space. Angular defects occur on length scales comparable to the radius of curvature. This phase transition is governed by a new strong curvature fixed point that obeys scaling below the upper critical dimension $d_{uc}=4$. The exponents of this fixed point are given by the leading orde…

通过弯曲空间调节玻璃形成液体的脆性

Tuning the fragility of a glassforming liquid by curving space

我们调查的空间曲率的影响，以及相关的“挫折”，在一个模型玻璃成型：双曲平面上的单原子液体的动力学。我们发现，系统的脆弱性，即温度变化的弛豫时间的敏感性，增加作为一个减少挫折。因此，弯曲的空间提供了一种调整脆弱性的方法，并使其尽可能大。我们还表明，新出现的“动态异质性”，缓慢放松系统的另一个显着特点的性质，是直接连接到挫折引起的拓扑缺陷的存在。

From glass formation to icosahedral ordering by curving three-dimensional space

Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass-formers, to tile space. Local icosahedral order however is strongly frustrated in Euclidean space, which obscures any causal relationship with the observed dynamical slowdown. Here we relieve frustration in a model glass-forming liquid by curving 3-dimensional space onto the surface of a 4-dimensional hypersphere. For sufficient curvature, frustration vanishes and the liquid freezes in a fully icosahedral structure via a sharp `transition'. Frus…

含阻挫的Ising模型中的高温调制、介观相互作用与超标度破缺：来自热力学几何的一些见解

High temperature modulations, meso-scale interactions and hyperscaling breakdown in Ising models with frustration: some insights from thermodynamic geometry

本研究重新审视A3NNI链，利用微观两点关联函数和宏观热力学曲率探测由竞争相互作用与阻挫引发的相行为，发现超标度破缺等现象，并澄清了高温关联长度的度量。