Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

Abstract

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of `+' or `$-$', `up' or `down', `yes' or `no'), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us to derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.

arXiv commentThis article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications

References in corpus (21)

• Critical phenomena in complex networks
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Percolation Critical Exponents in Scale-Free Networks
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Mean field solution of the Ising model on a Barabasi-Albert network
• Critical phenomena in networks
• Complex systems: physics beyond physics
• Supercondutor-Insulator Transition on Annealed Complex Networks
• Scaling Relations for Logarithmic Corrections
• Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Magnetization reversal in spin patterns with complex geometry
• Critical behavior of the Ising model in annealed scale-free networks
• Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks
• Ernst Ising - physicist and teacher
• Hidden geometry and dynamics of complex networks: Spin reversal in nanoassemblies with pairwise and triangle-based interactions
• Phase transitions in the Potts model on complex networks
• Ising model with variable spin/agent strengths
• Universal scaling relations for logarithmic-correction exponents
• Entropic equation of state and scaling functions near the critical point in scale-free networks
• Fisher Renormalization for Logarithmic Corrections

Cited by in corpus (6)

• A Master Equation for Power Laws
• Ising model on a $restricted$ scale-free network
• Individual bias and fluctuations in collective decision making: from algorithms to Hamiltonians
• Effective and asymptotic criticality of structurally disordered magnets
• Ising model with varying spin strength on a scale-free network: scaling functions and critical amplitude ratios
• Emergence of the 3D diluted Ising model universality class in a mixture of two magnets