We calculate mean square deviations for crystals in one and two dimensions. For the two dimensional lattices, we consider several distinct geometries (i.e. square, triangular, and honeycomb), and we find the same essential phenomena for each lattice structure. We investigate the stability of long-range crystalline order for a variety of coupling schemes, including short-range exponentially decaying inter-atomic potentials and long-range interactions with a power law dependence r^{-alpha}. For the latter in the 1D case, we find a critical value alpha_c(1D) = 1.615 +/- 0.005 for the power law decay exponent below which crystalline order is intact, and above which thermal fluctuations destroy long-range order when T > 0. The corresponding critical value for two dimensional lattices with displacements confined to the plane is alpha_c(2D) = 3.15 +/ 0.025. If motion perpendicular to the crystal plane is permitted, thermally induced distortions diverge rapidly (i.e. linearly) in dual layer systems with local stiffness provided by an extended coupling scheme, even if the interaction is long ranged, decaying as a power law in the separation between lattice sites.
Effect of crystal field and external magnetic field on the magnetic and thermodynamic properties of the Ising mixed spin (1-1/2-1) three layers system of cubic structure
Thermodynamic Relationships for Bulk Crystalline and Liquid Phases in the Phase-Field Crystal Model
我们提出的相场晶体（PFC）模型的自由能和流体静压下的体相的热力学状态变量之间的热力学关系。该关系是基于Larché和Cahn [Larché和Cahn，Acta Metallurgica，第21卷，1051（1973）]的结晶固体的热力学形式推导的。我们应用的关系来检查与不同的PFC模型的输入参数：温度，晶格间距，和PFC序参量，$\bar{n}$的平均值相关的热力学过程。散装结晶固体和液体相之间的平衡条件施加在PFC模型的热力学关系，以获得一个程序，用于确定固-液相共存。由此产生的程序被认为是一致的PFC社区中常用的方法，证明使用的共同切线建设，以确定固-液相共存的PFC模型。最后，我们将该程序应用于八阶拟合（Eighth Order-fit，EQF）PFC模型，该模型已被参数化为体心立方（$bcc$）Fe [Jaatinen et al.，Physical Review E 80，031602（2009）]，以演示该程序并开发关于PFC输入参数的物理直觉。我们表明，EOF-PFC模型参数化不预测稳定的$bcc$结构的正空位密度。这一结果表明PFC模型的另一种参数化，它需要两体直接关联函数的主峰位置作为$\bar{n}$的函数移动。
Thermodynamics, transition dynamics, and texturing in polymer-dispersed liquid crystals with mesogens exhibiting a direct isotropic/smectic-A transition
Computational Investigation of Reactivity Parameters, UV-Vis and IR Spectra, NLO Properties, and Temperature-Dependent Thermodynamic Characteristics of Schiff-Based Interdigitated 5O.m (m=14,16) Liquid Crystalline Compounds: A DFT Analysis
Thermodynamic evidence for nematic superconductivity in Cu$_x$Bi$_2$Se$_3$
非常规超导的特征在于宏观超导波函数的自发对称性破缺，以及规范对称性破缺，例如相对于基本晶格对称性的旋转对称性破缺。特别是，超导性与自发的旋转对称性破缺的波函数振幅，从而在体的性质，尚未报告以前，是有趣的，可以被称为“双”超导性的类比，以双液晶相。在这里，基于比热测量的单晶Cu $_x$ Bi $_2$ Se $_3$精确的磁场方向控制下，我们报告的热力学证据的超导性，即，明确的双重对称行为的三角晶格。结果表明，实现了一个“奇宇称”的状态，只有宏观量子凝聚体和不同的液晶中的双态。结果也证实了Cu $_x$ Bi $_2$ Se $_3$的拓扑非平凡超导电性。
