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Phase transitions in Ising models on directed networks.

Adam Lipowski¹, António Luis Ferreira², Dorota Lipowska³

¹Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 15, 2015

Summary

This summary is machine-generated.

We studied Ising models on directed networks, finding phase transitions in some lattices but not others. Directed random graphs require higher connectivity for ferromagnetic ordering compared to undirected ones.

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Area of Science:

Statistical mechanics
Complex networks
Condensed matter physics

Background:

Ising models are fundamental for understanding magnetism and phase transitions.
Heat-bath dynamics simulate thermal fluctuations in magnetic systems.
Network structure significantly influences model behavior.

Purpose of the Study:

To investigate the impact of directed network topology on Ising models with heat-bath dynamics.
To determine the conditions for ferromagnetic ordering and phase transitions in various directed networks.
To compare the behavior of Ising models on directed lattices and random graphs.

Main Methods:

Computational simulations of Ising models on directed triangular, cubic, and square lattices.
Analysis of Ising models on random directed graphs and out-homogeneous random graphs.
Examination of percolation and magnetic properties, including zero-temperature freezing.

Main Results:

Ising models on directed triangular and cubic lattices exhibit phase transitions within the Ising universality class.
The directed square lattice remains paramagnetic at all positive temperatures.
Directed random graphs require a higher connectivity threshold than undirected ones for ferromagnetic ordering.

Conclusions:

Network directionality critically alters ferromagnetic ordering and phase transition behavior.
Percolation of directed bonds does not inherently guarantee ferromagnetic ordering.
A specific connectivity threshold is necessary for finite-temperature ferromagnetic ordering in directed random graphs.