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

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.

References in corpus (9)

• Modularity and community structure in networks
• An efficient, multiple range random walk algorithm to calculate the density of states
• The Bethe lattice spin glass revisited
• Dynamics of Social Balance on Networks
• The energy landscape of social balance
• Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses
• Frustration - how it can be measured
• Ising antiferromagnet on the 2-uniform lattices
• Absence of an equilibrium ferromagnetic spin glass phase in three dimensions