Ising spin glass models versus Ising models: an effective mapping at high temperature II. Applications to graphs and networks

Abstract

By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.

11 pages, 1 Postscript figure

References in corpus (12)

• Statistical mechanics of complex networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Critical phenomena in networks
• Loops of any size and Hamilton cycles in random scale-free networks
• Principles of statistical mechanics of random networks
• Spin Glass Phase Transition on Scale-Free Networks
• On the number of circuits in random graphs
• Correlations in interacting systems with a network topology
• Ising spin glass models versus Ising models: an effective mapping at high temperature I. General result
• Mesoscopics and fluctuations in networks

Cited by in corpus (8)

• Critical phenomena in complex networks
• Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart
• First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory
• Effective field theory for models defined over small-world networks. First and second order phase transitions
• Critical behavior and universality in Levy spin glasses
• Ising spin glass models versus Ising models: an effective mapping at high temperature III. Rigorous formulation and detailed proof for general graphs
• Absence of small-world effects at the quantum level and stability of the quantum critical point
• Forest expansion of two-body partition functions for sparse interaction graphs