论文标题
超冷液体和玻璃过渡的热和动态特性的iSing模型
An Ising model for the thermal and dynamic properties of supercooled liquids and the glass transition
论文作者
论文摘要
我们描述了具有正交动力学的Ising模型的行为，在同一蒙特卡洛（MC）步骤中，能量变化和对齐方式的变化永远不会发生。这种正交模型（OIM）允许能量保护和动量保护，以自己的首选时间尺度独立进行。 MC对OIM模拟模拟模拟了二十多个独特的特征，这些特征通常在玻璃温度上方和下方发现。例子包括特定的热量，该热量在TG周围具有磁滞，表现出原发峰和次级峰的相位损失，Alpha响应时间的Super-Arrhenius t依赖性以及随着系统大小的增加（N）而增加的脆弱性。 OIM中能量波动的平均场理论可为超级阿内乌斯发散带来新的表达。因为这种差异让人联想到vogel-fulcher-tammann（VFT）法律，所以我们称其为VFT2法律。将VFT2定律线性化的修改式Stickel图与在五个玻璃形成液体上的主要反应（来自文献）的测量（来自文献）的测量在定性上保持一致。与OIM的这种一致性表明，几个基本特征控制了超冷液体。将液体冻结到玻璃中的冻结涉及通过有限尺寸效应扩大的基础二阶转变。 VFT2定律来自能量波动，通过熵瓶颈增强了途径，而不是在能量屏障上激活。主要响应时间与n逆n呈指数差异，这与测量结果得出的松弛时间的分布一致。通过主要响应的t依赖性发现的系统尺寸类似于通过核磁共振与简单分子玻璃形成液体测量的独立放松区域的大小。 OIM为更详细的液态玻璃行为模型提供了广阔的基础。
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.
