Generating droplets in two-dimensional Ising spin glasses by using matching algorithms

TL;DR

This paper investigates droplet behavior in two-dimensional Ising spin glasses using an exact matching algorithm, enabling analysis of larger systems and revealing insights into droplet energy scaling and size behavior.

Contribution

It introduces the use of an exact matching algorithm for studying droplets in 2D Ising spin glasses, highlighting its advantages and limitations compared to previous methods.

Findings

Large system sizes up to L=240 analyzed

Scaling behavior suggests compatibility with droplet theory for large sizes

Limitations in analyzing first excitations due to system size constraints

Abstract

We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.