How to simulate phase separation in discrete system using LAMMPS?

I would like to simulate phase separation in LAMMPS. I am looking for advice on what kind of 2 atom system and interactions will experience a phase separation.

A continuous phase flow model given by CahnâHilliard equation:
$$frac{partial c}{partial t} = Dnabla^2mu \ mu = left(c^3-c-gammanabla^2 cright)\ c – text{concentration}\ mu – text{chemical potential}\$$

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I tried to use a discrete two atom system in LAMMPS. One type of the particles has a LJ interaction and the second type has a soft potential. Between the 2 type distinct particles there is also a soft potential:

Initial configuration (interleaved lattice of the two particles):

Steady state configuration at $$T=0.1$$ (reduced LJ units):

Configuration file:

``````units lj

timestep 0.001

dimension 2
boundary p p p
atom_style atomic
neighbor 0.3 bin
neigh_modify every 20 delay 0 check no

variable temp equal 0.1

lattice hex 0.5
region simbox block 0 50 0 25 -0.1 0.1
create_box 2 simbox

lattice hex 0.5
create_atoms 1 region simbox

lattice hex 0.5 origin 0.5 0.5 0
create_atoms 2 region simbox

mass 1 1
mass 2 1.0

velocity all create \${temp} 1234567 dist gaussian
pair_style hybrid lj/cut 2.5 soft 0.5
pair_coeff 1 1 lj/cut 2.0 0.8 4.0

pair_coeff 1 2 soft 0.5
pair_coeff 2 2 soft 0.5

fix 1 all nvt temp $${temp}$${temp} 0.1

dump 1 all atom 500 out/dump_temp_\${temp}.lammpstrj
write_data data.all
thermo 500
run 500000
``````

1. How can I make my system look more similar to the continuous model by Cahn and Hiliard? I want to get a more prominent phase separation like in the continuous model. I am not sure how to calibrate my system/interactions.
2. Is there a different simple system I can use to simulate phase separation?