Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder

TL;DR

This study numerically investigates how ground state configurations in disordered models behave as system size grows, providing evidence for the two-state picture and analyzing convergence properties in finite samples.

Contribution

It offers the first numerical evidence supporting the two-state picture for ground states in models with quenched disorder and analyzes convergence scaling in finite systems.

Findings

Configurations in fixed-size windows converge to a unique state.

Convergence scaling aligns with fractal dimension of domain walls.

Large windows are needed for convergence in 3D systems.

Abstract

The effect of open boundary conditions for four models with quenched disorder are studied in finite samples by numerical ground state calculations. Extrapolation to the infinite volume limit indicates that the configurations in ``windows'' of fixed size converge to a unique configuration, up to global symmetries. The scaling of this convergence is consistent with calculations based on the fractal dimension of domain walls. These results provide strong evidence for the ``two-state'' picture of the low temperature behavior of these models. Convergence in three-dimensional systems can require relatively large windows.