Annealed inhomogeneities in random ferromagnets.

Area of Science:

• Statistical physics
• Network science
• Complex systems

Background:

• Spin models like the Ising model are crucial for understanding social and technological systems.
• The behavior of these models on annealed networks (with fluctuating edges) is less understood than on quenched networks.

Purpose of the Study:

• To investigate the annealed ferromagnetic Ising model on complex random networks.
• To analyze how annealing affects critical temperatures and exponents in Erdős-Rényi and configuration models.
• To understand the impact of fluctuating network structures on phase transitions.

Main Methods:

• Studied the annealed ferromagnetic Ising model on Erdős-Rényi random networks.
• Analyzed the annealed Ising model on configuration models with prescribed degree distributions.
• Investigated networks with Poissonian degrees and deterministic degrees.

Main Results:

• Annealed networks exhibit distinct critical temperatures, with some finite even when the quenched critical temperature is infinite.
• The Ising model's interaction with fluctuating edges alters the degree distribution.
• Critical exponents in the configuration model with deterministic degrees match quenched universality classes; however, annealing in random degree configuration models eliminates power-law critical exponents.

Conclusions:

• The annealed Ising model on complex networks displays unique critical phenomena not observed in quenched systems.
• Network annealing significantly influences phase transitions and critical behavior, particularly in models with random degrees.
• Understanding annealed network dynamics is essential for accurately modeling real-world systems.