A unifying model for several two-dimensional phase transitions

TL;DR

This paper introduces a unified model based on quantum percolation and dephasing that captures the critical physics of various two-dimensional phase transitions, including quantum Hall and metal-insulator transitions.

Contribution

It presents a simple, physically transparent model that unifies multiple two-dimensional phase transitions and computes crossover functions using real space renormalization group techniques.

Findings

Unified phase diagram for multiple 2D transitions

Calculated crossover functions between critical points

Analyzed critical behavior and addressed experimental puzzles

Abstract

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator", classical percolation and, to some extent, superconductor-insulator transitions. Using real space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.