A challenge for critical point of spin glass in ground state

TL;DR

This paper introduces a duality-based method to accurately identify the critical point in the ground state of random spin systems, including spin glasses, offering a new analytical approach for such complex systems.

Contribution

It proposes a novel equality for pinpointing the critical point in the ground state, validated on bond-dilution Ising models across various lattices.

Findings

Exact critical points for bond-dilution Ising models determined

Duality analysis effective at zero temperature

Provides new insights into spin glass ground states

Abstract

We show several calculations to identify the critical point in the ground state in random spin systems including spin glasses on the basis of the duality analysis. The duality analysis is a profound method to obtain the precise location of the critical point in finite temperature even for spin glasses. We propose a single equality for identifying the critical point in the ground state from several speculations. The equality can indeed give the exact location of the critical points for the bond-dilution Ising model on several lattices and provides insight on further analysis on the ground state in spin glasses.