Metal-Insulator Transition in Two- and Three-Dimensional Logarithmic Plasmas

We consider the scaling of the mean square dipole moment in a plasma with logarithmic interactions in a two- and three-dimensional systems. In both cases, we establish the existence of a low-temperature regime where the mean square dipole moment does not scale with system size and a high-temperature regime where it does scale with system size. Thus, there is a nonanalytic change in the polarizability of the system as a function of temperature and hence a metal-insulator transition in both cases. The relevance of this transition in three dimensions to quantum phase transitions in $(2+1)$-dimensional systems is briefly discussed.

Figure 1

Results from MC simulations of the 2DCG, where $1.0\times {10}^5\mathrm{\text{sweeps}}$ were used at each temperature. (a) $⟨s^2⟩$ versus $T$ for a selection of the simulated system sizes $L=8$, 12, 16, 20, 24, 28, 32, 36, 40, and 48. Error bars are smaller than the symbols used. (b) $\alpha$ versus $T$ found from fitting the data of $⟨s^2⟩$ at different $T$ to $A{L}^{\alpha }$, where $A$ is a constant. A selection of such fits are shown in (c). We note that $⟨s^2⟩$ is practically independent of $L$ up to a certain $T$.

Figure 2

Results from simulations of the 3DLG. Up to $2.0\times {10}^5\mathrm{MC}$ sweeps were used at each temperature. (a) $⟨s^2⟩$ vs $T$ for some of the simulated system sizes $L=8$, 12, 16, 20, 24, 28, 32, 36, and 40. Error bars are smaller than the symbols used. (b) $\alpha (T)$ vs $T$ found from fitting the data of $⟨s^2⟩$ at different $T$ to $A{L}^{\alpha }$, where $A$ is a constant. A selection of such fits are shown in (c). It is evident that a low-temperature regime where $⟨s^2⟩$ is independent of $L$ exists in the 3D log gas in the same way that it exists in the 2D log gas.