How motility affects Ising transitions

TL;DR

This paper investigates how particle motility influences phase separation in a lattice gas model with internal orientations, revealing that increased motility raises the interaction threshold for phase transition and impedes cluster formation.

Contribution

It introduces a lattice gas model with internal orientations and analyzes how motility affects phase transitions, showing motility delays cluster formation and modifies critical interaction strength.

Findings

Phase transition occurs at higher interaction strength with increased motility.

Motility impedes cluster formation, requiring stronger attraction.

No phase separation occurs at zero interaction regardless of motility.

Abstract

We study a lattice gas model of hard-core particles on a square lattice experiencing nearest neighbour attraction $J$. Each particle has an internal orientation, independent of the others, that point towards one of the four nearest neighbour and it can move to the neighbouring site along that direction with the usual Metropolis rate if the target site is vacant. The internal orientation of the particle can also change to any of the other three with a constant rate $\omega.$ The dynamics of the model in $\omega\to \infty$ reduces to that of the Lattice Gas (LG) which exhibits a phase separation transition at particle density $\rho=\frac12$ and temperature $T=1,$ when the strength of attraction $J$ crosses a threshold value $\ln(1+ \sqrt{2}).$ This transition belongs to Ising universality class. For any finite $\omega>0,$ the particles can be considered as attractive run-and-tumble particles (RTPs) in two dimensions with motility $\omega^{-1}.$ We find that RTPs also exhibit a phase separation transition, but the critical interaction required is $J_c(\omega)$ which increases monotonically with increased motility $\omega^{-1}.$ It appears that the transition belongs to Ising universality class. Surprisingly, in these models, motility impedes cluster formation process necessitating higher interaction to stabilize microscopic clusters. Moreover, MIPS like phases are not found when $J=0.$