A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation

TL;DR

This work analyzes a driven, coupled two-species system with vacancies (LHV model) on a fluctuating landscape, revealing how neutral vacancies qualitatively reshape the competition between aligned and reverse biases. Through mean-field flux-balance calculations and a mapping to a one-dimensional partially asymmetric exclusion process in the maximal current regime, the authors identify two novel ordered phases: FPPS, with one species forming a macroscopic hill or valley and the other coexisting with vacancies, and VIPS, where the plateaus beneath the phase-separated species exhibit a height that scales as $\sqrt{N}$ and include a small admixture of the other species. The findings show that vacancies enable long-range order even when opposite bias is strong, and they unveil a plateau-based mechanism for phase ordering distinct from previously known LH phases. These results highlight a crucial role for vacancies in nonequilibrium coupling and offer insights transferable to other landscape-coupled driven systems.

Abstract

We study a coupled driven system where two different species of particles, along with some vacancies or holes, move on a landscape whose shape fluctuates with time. The movement of the particles is guided by the local shape of the landscape, and this shape is also affected by the presence of different particle species. When a particle species push the landscape in the same (opposite) direction of its own motion, it is called an aligned (a reverse) bias. Aligned bias promotes ordering while reverse bias destroys it. In absence of vacancies, the system reduces to previously studied LH model with different kinds of ordered and disordered phases which could be explained as a competition or cooperation between aligned bias and reverse bias. This interplay is expected to remain unaffected even when vacancies are present since vacancies do not impart any kind of bias on the landscape. However, we find presence of vacancies effectively weakens the reverse bias and this significantly changes the outcome of the competition between the two bias types. As a result novel ordered phases emerge which were not seen before. We analytically calculate the new phase boundaries within mean field approximation. We show even when aligned bias is weaker than reverse bias, it is possible to find long range order in the system. We discover two new phases where particle species showing weak aligned bias phase separate and the other species with strong reverse bias stays mixed with the vacancies. We call these phases finite current with partial phase separation (FPPS) and vacancy induced phase separation (VIPS). The landscape beneath the phase separated species takes the form of a macroscopic hill or valley in FPPS phase. But in VIPS phase it has the shape like a plateau whose height scales as square root of system size. The landscape in the remaining part of the system is disordered in both these phases.

Figures (10)

• Figure 1: Mapping onto a height model. Heavy, light particles and holes are respectively shown as red, yellow and blue circles. Upslope and downslope bonds are depicted by $\slash$ and $\backslash$ respectively.
• Figure 2: Transition rules between the local hills and valleys of the landscape occupied by either $H$, $L$ particles or holes. Here $-\frac{1}{2} \leq b, b' \leq \frac{1}{2}$.
• Figure 3: Transition rules for the particles where $0 < a \leq \frac{1}{2}$.
• Figure 4: LH model phase diagram and representative configuration in each phase. The colours red, and yellow represents $H$, and $L$ particles, respectively. The values of $b,b'$ are as follows.(b) SPS, $b = b' = 0.4$; (c) IPS, $b' = 0.4$, $b = 0$; (d) FPS, $b' = 0.4$, $b = -0.1$; (e) FDPO, $b' = 0.4$, $b = -0.4$; (f) disordered phase, $b = b' = -0.4$. Here, $N = 1026$, $\rho_{H} = \rho_{L} = 1/2$ and $a = 0.4$. This phase diagram is valid for any finite density of heavy and light particle at thermodynamic limit, $N \to \infty$.
• Figure 5: Phase diagram for LHV model and representative configurations in each phase. The colours red, yellow and blue represent $H$, $L$ particle and hole, respectively. The values of $b,b'$ are as follows: (b) SPS, $b = b' = 0.4$; (c) IPS, $b' = 0.4$, $b = 0$; (d) FPPS, $b' = 0.4$, $b = -0.1$; (e) VIPS, $b' = 0.18$, $b = -0.4$; (f) disordered phase, $b = b' = -0.4$. All representative configurations are shown for $N = 1026$, $\rho_{H} = \rho_{L} = 1/3$ and $a = 0.4$. The phase diagram is valid for any finite density of different particle species and vacancies at the thermodynamic limit, $N \to \infty$.