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

TL;DR

This paper investigates the metal-insulator transition in 2D and 3D logarithmic plasmas by analyzing dipole moment scaling, revealing a nonanalytic transition related to polarizability changes at different temperatures.

Contribution

It demonstrates the existence of a metal-insulator transition in 2D and 3D logarithmic plasmas through scaling analysis of dipole moments, highlighting a nonanalytic change in polarizability.

Findings

Existence of low-temperature regime with size-independent dipole moments

High-temperature regime with size-dependent dipole moments

Identification of a nonanalytic transition in polarizability

Abstract

We consider scaling of the mean square dipole moments in a plasma with logarithmic interactions in a two- and three-dimensional system. 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.