Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions

Abstract

The phase diagram of two-dimensional continuous particle systems is studied using the event-chain Monte Carlo algorithm. For soft disks with repulsive power-law interactions ∝r^{-n} with n≳6, the recently established hard-disk melting scenario (n→∞) holds: a first-order liquid-hexatic and a continuous hexatic-solid transition are identified. Close to n=6, the coexisting liquid exhibits very long orientational correlations, and positional correlations in the hexatic are extremely short. For n≲6, the liquid-hexatic transition is continuous, with correlations consistent with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario. To illustrate the generality of these results, we demonstrate that Yukawa particles likewise may follow either the KTHNY or the hard-disk melting scenario, depending on the Debye-Hückel screening length as well as on the temperature.

Hard-sphere melting and crystallization with event-chain Monte Carlo

“…Considerable speedup was also demonstrated for the extension of ECMC to continuous potentials 13,14 . In this paper, we assess the speed of ECMC, EDMD, and LMC not by computing autocorrelation functions in equilibrium, but rather by the time scales associated with melting and crystallization in systems of many spheres at high density.…”

Thermodynamics of Yukawa fluids near the one-component-plasma limit

“…4 are the numerical data for the thermal energy of the fluid with inverse power law (IPL) interaction, V (r) = ǫ(σ/r) n , with n = 6 [34]. To produce this plot we have used the notation Γ ≡ (ǫ/T )(σ/a) n , and took Γ m ≃ 105.9 at the fluid-solid phase transition (in fact, this is the fluid-hexatic transition) [35]. We see that the universal scaling only holds for sufficiently soft interactions, which is not the case for the IPL n = 6 case (the thermal energy is systematically lower).…”

Colloidal Crystallization in 2D for Short-Ranged Attractions: A Descriptive Overview

“…As mentioned in the introduction, with the exception of some works [12][13][14][15] which find a first order transition, most researchers find two phase transitions with a hexatic phase in between the fluid and the crystal phases, in accord with the KTHNY theory [27][28][29]. Some researchers find the two transitions to be continuous [16][17][18][19][20][21], while some others [22][23][24][25][26] find one or the two transitions to be first order (indicating a coexistence of the phases at the transition point), depending on the repulsive interaction potential. To inquire about the crossover from a crystallization transition for a sudden quench-as described in the last paragraph-to a KTHNY type of transition for a very slow cooling rate, Deutschländer et al [142] have studied the crystallization process when varying the cooling rate by three orders of magnitude.…”

“…In this last case the situation is not quite clear since, with the exception of some studies (e.g., [12][13][14][15]) that find a first order transition from the liquid to the solid or vice versa, most researchers find two phase transitions with a hexatic phase in between the fluid and the crystal phases. However, some of them find the two transitions to be continuous [16][17][18][19][20][21], while some others [22][23][24][25][26] find one or the two transitions to be first order (indicating a coexistence of the phases at the transition point), depending on the repulsive interaction potential. The two continuous phase transitions scenario was predicted by the celebrated KTHNY theory, after Kosterlitz and Thouless [27], Halperin and Nelson [28], and Young [29].…”