Conductivity of a lattice gas model. Monte-Carlo simulations

A lattice-gas model, which has conductors connecting each pair of occupied nearest-neighbour sites, is studied using Monte-Carlo simulations. At low temperatures, the lattice-gas atomic density approaches unity and the system is in a high-conductivity state. At high temperatures, the lattice-gas atomic density approaches 0.5 and the system is in a low-conductivity state. On a square lattice, the conductivity of the system in the low-conductivity state goes to zero. On a simple cubic lattice however, the conductivity of the system in the low-conductivity state approaches a non-zero constant value. The liquid-gas-transition temperature and the high-low-conductivity transition temperatures appear to be the same from our numerical simulations.