Steady states of a nonequilibrium lattice gas

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicritical point.

Figure 1

Phase diagram in $f$ and $T$ for $E=2.0$. Triangles and diamonds are boundaries in the $40\times 40$ system; ×’s are for the $60\times 60$ system.

Figure 2

(Color online) Configurations of the $40\times 40$ lattice at $f=0.075$, $E=2.0$ for four temperatures. Upper left, $T=1.77$; upper right, $T=0.95$; lower left, $T=0.84$; lower right, $T=0.78$.

Figure 3

$S(0,1)$ as a function of $T$ for $f=0.50$, $E=2.0$. Open (solid) triangles are for the $40\times 40(60\times 60)$ system.

Figure 4

$\Delta (0,1)$ as a function of $T$ for $f=0.50$, $E=2.0$. Open (solid) triangles are for the $40\times 40(60\times 60)$ system.

Figure 5

$S(0,1)$ and $S(1,0)$ as a function of $T$ for $f=0.075$, $E=2.0$ in the $40\times 40$ system. Triangles [squares] are for $S(0,1)\left[S(1,0)\right]$. Lines and dashes are provided to guide the eye.

Figure 6

$\Delta (0,1)$ as a function of $T$ for $f=0.075$, $E=2.0$. Open (solid) triangles are for the $40\times 40(60\times 60)$ system.

Figure 7

Time trace at $T=0.832$, $E=2.0$, $f=0.075$, in the $40\times 40$ system. Time in units of $2\times {10}^5$ MCS is plotted on the horizontal axis. The values of $s(0,1)$ and $s(1,0)$ (triangles and squares, respectively) are plotted on the vertical axis.

Figure 8

(Color online) Configurations for several $f$ at $E=20.0$, $T=2.0$, in the $40\times 40$ system. Upper left, $f=0.50$; upper middle, $f=0.10$; upper right, $f=0.075$; lower left, $f=0.05$; lower middle, $f=0.04$; lower right, $f=0.025$.

Figure 9

Phase diagram in $f$ and $E∕T$ at $T=2.0$, in the $40\times 40$ system. Disorder (DO) is observed at small $f$ and $E$; the transverse strip (TS) dominates at high $f$ and $E$. The error bars are smaller than the size of the data points, unless indicated.

Figure 10

$S(0,1)$ as a function of $E∕T$ for several $f$ in the $40\times 40$ system: $f=0.50$, diamonds; $f=0.10$, squares; $f=0.075$, triangles; $f=0.05$, circles; $f=0.04$, +’s; $f=0.025$, ×’s.

Figure 11

$\Delta (0,1)$ as a function of $E∕T$, in the $40\times 40$ system, for several $f$. The symbols are the same as in the previous figure. A line has been added to the $f=0.075$ data to guide the eye.

Figure 12

Phase diagram in $E∕T$ and $f$ for $T=1.2$, in the $40\times 40$ system. A continuous boundary separates DO from TS (diamonds) as well as DO from PS (triangles). ×’s indicate a possible boundary between TS and PS. A few typical error bars are shown.

Figure 13

(Color online) Typical configurations for the $T=1.2$ plane, in the $40\times 40$ system. Upper left, $f=0.075$, $E=20.0$; upper right, $f=0.05$, $E=20.0$; lower left, $f=0.075$, $E=4.0$; lower right, $f=0.05$, $E=2.4$.

Figure 14

$S(0,1)$ as a function of $E∕T$, in the $40\times 40$ system for several $f$. $f=0.50$, diamonds; $f=0.10$, squares; $f=0.075$, solid triangles. Open triangles indicate $S(1,0)$ for $f=0.075$.

Figure 15

$\Delta (0,1)$ (solid triangles) and $\Delta (1,0)$ (open triangles) as a function of $E∕T$ in the $40\times 40$ system for $f=0.075$.

Figure 16

$S(0,1)$ as a function of effective drive for $J=1$, $f=0.50$. System sizes: $40\times 40$, open triangles; $40\times 60$, circles; $40\times 80$, ×’s; $60\times 60$, solid triangles; $60\times 80$, squares. Lines have been added to the largest and smallest systems to guide the eye.

Figure 17

$\Delta (0,1)$ as a function of effective drive for $J=1$, $f=0.50$. The symbols are the same as in the previous figure.

Figure 18

The phase diagram in the $f\text{−}T$ plane, $E=2.0$, with $f$ rescaled to represent the number of rows of the minority species. System sizes: solid triangles, $40\times 40$; ×’s, $60\times 60$; squares, $60\times 80$.

Figure 19

Anisotropic scaling plot of $S(1,0)$ at $f=0$, $E=2.0$. System sizes: squares, $24\times 54$; ×’s, $28\times 86$; triangles, $32\times 128$.