Two Information Entropies of Square-Lattice $\pm {J}$ Ising Models

TL;DR

This paper introduces two novel information entropies based on local energy and spin configurations to distinguish spin glass states from paramagnetic states in square-lattice $\,J$ Ising models, revealing insights into their ordering and disordering behaviors.

Contribution

The study proposes and applies two new information entropies, $S_{IB}$ and $S_{IS}$, to analyze phase states in $\,J$ Ising models, providing a clearer distinction between spin glass and paramagnetic states.

Findings

$S_{IB}$ and $S_{IS}$ effectively distinguish spin glass from paramagnetic states.

Spin glass states show ordering in bonding energy but disorder in spin orientations.

$S_{IB}$ aligns with thermodynamic entropy, indicating its reliability.

Abstract

Two information entropies, $S_{IB}$ based on the local bonding energy configurations and $S_{IS}$ based on the local spin configurations, are applied in the square-lattice $\pm {J}$ Ising systems with Monte Carlo simulations. With $S_{IB}$ and $S_{IS}$, the spin glass states can be distinguished from paramagnetic states clearly. The results reveal that the nature of spin glass states is of ordering in bonding energy and disordering in spin orientations. The consistence of $S_{IB}$ and the thermodynamic entropy is found.