Frustration of signed networks: How does it affect the thermodynamic properties of a system?

TL;DR

This paper investigates how frustration in signed networks, caused by negative interactions, influences the thermodynamic properties and phase transitions of the Edwards-Anderson Ising model across various network structures.

Contribution

It provides a quantitative analysis of network frustration and its linear relationship with critical temperature, validated by theoretical and numerical methods.

Findings

Frustration decreases the critical temperature linearly.

Mean-field theory accurately predicts the frustration-temperature relationship.

Numerical simulations confirm theoretical predictions.

Abstract

Signed networks with positive and negative interaction are widely observed in the real systems. The negative links would induce frustration, then affect global properties of the system. Based on previous studies, frustration of signed networks is investigated and quantified. Frustrations of $\pm J$ (Edwards-Anderson) Ising model with a concentration $p$ of negative bonds, constructed on different networks, such as triangular lattice, square lattice and random regular networks (RRN) with connectivity $k=6$ are estimated by theoretical and numerical approaches. Based on the quantitative measurement of frustration, its effects on phase transitions characterized by order parameter $q_{EA}$ are studied. The relationship of critical temperature $T_c$ with the quantified frustration $\mu$ is given by mean-field theory. It shows that $T_c$ decreases linearly with frustration $\mu$ . The theory is checked by numerical estimations, such as the Metropolis algorithm and Replica Symmetric Population Dynamics Algorithm. The numerical estimates are consistent well with the mean-field prediction.