Center for Superfunctional Materials, Department of Chemistry and Department of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea.
Phys Rev E. 2019 Feb;99(2-1):022145. doi: 10.1103/PhysRevE.99.022145.
In two-dimensional Lennard-Jones (LJ) systems, a small interval of melting-mode switching occurs below which the melting occurs by first-order phase transitions in lieu of the melting scenario proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). The extrapolated upper bound for phase coexistence is at density ρ∼0.893 and temperature T∼1.1, both in reduced LJ units. The two-stage KTHNY scenario is restored at higher temperatures, and the isothermal melting scenario is universal. The solid-hexatic and hexatic-liquid transitions in KTHNY theory, even so continuous, are distinct from typical continuous phase transitions in that instead of scale-free fluctuations, they are characterized by unbinding of topological defects, resulting in a special form of divergence of the correlation length: ξ≈exp(b|T-T_{c}|^{-ν}). Here such a divergence is firmly established for a two-dimensional melting phenomenon, providing a conclusive proof of the KTHNY melting. We explicitly confirm that this high-temperature melting behavior of the LJ system is consistent with the melting behavior of the r^{-12} potential and that melting of the r^{-n} potential is KTHNY-like for n≤12 but melting of the r^{-64} potential is first order; similar to hard disks. Therefore we suggest that the melting scenario of these repulsive potentials becomes hard-disk-like for an exponent in the range 12<n<64.
在二维 Lennard-Jones（LJ）体系中，在一个较小的熔化模式切换区间内，熔化发生的方式是通过一级相变而不是 Kosterlitz、Thouless、Halperin、Nelson 和 Young（KTHNY）提出的熔化情景。在约 0.893 的密度 ρ和约 1.1 的温度 T 的约化 LJ 单位中，相共存的外推上限。在较高温度下恢复了两阶段 KTHNY 情景，等温熔化情景是普遍的。即使如此，KTHNY 理论中的固体-六方和六方-液体转变都是连续的，但与典型的连续相变不同，它们的特征不是无标度涨落，而是拓扑缺陷的解绑，导致相关长度的特殊形式发散：ξ≈exp(b|T-T_{c}|^{-ν})。在这里，二维熔化现象中确立了这种发散，为 KTHNY 熔化提供了确凿的证据。我们明确证实，LJ 系统的这种高温熔化行为与 r^{-12}势的熔化行为一致，并且 r^{-n}势的熔化对于 n≤12 是 KTHNY 型的，但 r^{-64}势的熔化是一级相变；类似于硬磁盘。因此，我们建议对于指数在 12<n<64 的范围内，这些排斥势的熔化情景变得类似于硬磁盘。
