Magnetic models on various topologies

Abstract

A brief review is given on the study of the thermodynamic properties of spin models defined on different topologies like small-world, scale-free networks, random graphs and regular and random lattices. Ising, Potts and Blume-Capel models are considered. They are defined on complex lattices comprising Appolonian, Barabási-Albert, Voronoi-Delauny and small-world networks. The main emphasis is given on the corresponding phase transitions, transition temperatures, critical exponents and universality, compared to those obtained by the same models on regular Bravais lattices.

4 pages. Brazilian Meeting on Simulational Physics

References in corpus (9)

• Majority-vote model on directed Erdos-Renyi random graphs
• Contact process on a Voronoi triangulation
• Ising model on the Apollonian network with node dependent interactions
• q-state Potts model on the Apollonian network
• Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay random lattices
• Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder
• Ising model with spins S=1/2 and 1 on directed and undirected Erdös-Rényi random graphs
• Non-Universality in Semi-Directed Barabasi-Albert Networks
• Potts model with $q=4,6,$ and 8 states on Voronoi-Delaunay random lattice

Cited by in corpus (3)

• Ising Model on a random network with annealed or quenched disorder
• Two-dimensional Ising model on random lattices with constant coordination number
• Universality of continuous phase transitions on random Voronoi graphs