We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of momentum to proceed independently, on their own preferred time scales. MC simulations of the OIM mimic more than twenty distinctive characteristics that are commonly found above and below the glass temperature, Tg. Examples include a specific heat that has hysteresis around Tg, out-of-phase loss that exhibits primary and secondary peaks, super-Arrhenius T dependence for the alpha response time, and fragilities that increase with increasing system size (N). Mean-field theory for energy fluctuations in the OIM yields a novel expression for the super-Arrhenius divergence. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann (VFT) law squared, we call it the VFT2 law. A modified Stickel plot, which linearizes the VFT2 law, gives qualitatively consistent agreement with measurements of primary response (from the literature) on five glass-forming liquids. Such agreement with the OIM suggests that several basic features govern supercooled liquids. The freezing of a liquid into a glass involves an underlying 2nd-order transition that is broadened by finite-size effects. The VFT2 law comes from energy fluctuations that enhance the pathways through an entropy bottleneck, not activation over an energy barrier. Primary response times vary exponentially with inverse N, consistent with the distribution of relaxation times deduced from measurements. System sizes found via the T dependence of the primary response are similar to sizes of independently relaxing regions measured by nuclear magnetic resonance for simple-molecule glass-forming liquids. The OIM provides a broad foundation for more-detailed models of liquid-glass behavior.

中文翻译：

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过冷液体的热和动态特性以及玻璃化转变的 Ising 模型

我们描述了具有正交动力学的 Ising 模型的行为，其中能量的变化和对齐的变化永远不会在同一个蒙特卡洛 (MC) 步骤中发生。这种正交伊辛模型（OIM）允许能量守恒和动量守恒在它们自己喜欢的时间尺度上独立进行。OIM 的 MC 模拟模拟了 20 多个不同的特征，这些特征通常在玻璃温度 Tg 上下发现。示例包括在 Tg 附近具有滞后的比热、表现出初级和次级峰值的异相损耗、对 alpha 响应时间的超阿伦尼乌斯 T 依赖性以及随着系统尺寸 (N) 的增加而增加的脆弱性。OIM 中能量波动的平均场理论产生了超阿伦尼乌斯散度的新表达式。因为这种分歧让人想起 Vogel-Fulcher-Tammann (VFT) 平方定律，我们将其称为 VFT2 定律。将 VFT2 定律线性化的修正 Stickel 图与对五种玻璃形成液体的主要响应测量值（来自文献）给出了定性一致的一致性。与 OIM 的这种协议表明，有几个基本特征支配过冷液体。将液体冻结成玻璃涉及潜在的二阶跃迁，该跃迁因有限尺寸效应而变宽。VFT2 定律来自能量波动，它通过熵瓶颈增强路径，而不是通过能量屏障激活。主要响应时间随 N 的倒数呈指数变化，这与从测量中推导出的弛豫时间分布一致。通过初级响应的 T 依赖性发现的系统大小类似于通过核磁共振测量的单分子玻璃形成液体的独立弛豫区域的大小。OIM 为更详细的液态玻璃行为模型提供了广泛的基础。