Anomalous Melting Scenario of the Two-Dimensional Core-Softened System

We present a computer simulation study of the phase behavior of two-dimensional (2D) classical particles repelling each other through an isotropic core-softened potential. As in the analogous three-dimensional (3D) case, a reentrant-melting transition occurs upon compression for not too high pressures, along with a spectrum of waterlike anomalies in the fluid phase. However, in two dimensions in the low density part of the phase diagram melting is a continuous two-stage transition, with an intermediate hexatic phase. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young scenario for this melting transition. On the other hand, at the high density part of the phase diagram one first-order transition takes place.

Figure 1

(a) Phase diagram of the system with the potential (1) in the $\rho \text{−}T$ plane, where the triangular ($T$) and square ($S$) phases are shown. Inset: the potential Eq. (1). (b) Phase diagram of the same system in the $\rho \text{−}T$ plane.

Figure 2

The low-temperature set of isotherms. Results are for temperatures $T=0.12$, 0.14, 0.16, 0.20, 0.22, 0.24, 0.26 from bottom up. Inset: the high-temperature set of isotherms. The lines correspond to temperatures $T=0.32$, 0.38, 0.45, 0.55, 0.65 from bottom to top.

Figure 3

(a) Orientational order parameter as a function of density for different temperatures. (b) The corresponding susceptibility ${\chi }_6$ as a function of density for different temperatures.

Figure 4

(a) OPs ${\psi }_T$ and ${\psi }_6$ as functions of temperature for $\rho =0.56$. It is clearly the narrow hexatic phase. (b) The low-density part of the phase diagram [Fig. 1] along with the lines of solid-hexatic and hexatic-liquid transitions.

Figure 5

Log-log plots of the orientational correlation function $G_6(r)$ at selected densities across the hexatic region for $T=0.12$. Upon increasing $\rho$ from 0.41 to 0.45 there is a qualitative change in the large-distance behavior of $G_6(r)$, from constant (solid) to power-law decay (hexatic fluid), up to exponential decay (normal fluid). Note that, consistently with the KTHNY theory, the decay exponent $\eta$ is less than $1/4$ for $\rho >0.43$.