A new method for analyzing ground-state landscapes: ballistic search

TL;DR

The paper introduces a 'ballistic-search' algorithm to identify and analyze clusters of ground states in Ising spin glasses, enabling insights into their landscape structure for moderate system sizes.

Contribution

It presents a novel algorithm for identifying ground-state clusters in spin glasses and applies it to analyze the structure of 2D ±J spin glasses.

Findings

Identified ground-state clusters in systems up to size L=20.

Estimated the ground-state entropy per spin as s_0=0.086(4)k_B.

Demonstrated the method's effectiveness across different system sizes.

Abstract

A ``ballistic-search'' algorithm is presented which allows the identification of clusters (or funnels) of ground states in Ising spin glasses even for moderate system sizes. The clusters are defined to be sets of states, which are connected in state-space by chains of zero-energy flips of spins. The technique can also be used to estimate the sizes of such clusters. The performance of the method is tested with respect to different system sizes and choices of parameters. As an application the ground-state funnel structure of two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by calculating a huge number of ground states per realization. A T=0 entropy per spin of s_0=0.086(4)k_B is obtained.