One-dimensional Ising model built on small-world networks: competing dynamics
arXiv:cond-mat/0505340 · doi:10.1103/PhysRevE.71.056123
Abstract
In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result of rewiring-type is given because of the similarities of these two typical networks. We study the dynamical processes with competing Glauber mechanism and Kawasaki mechanism. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. By studying the phase diagram obtained in the present work, we can realize some dynamical properties influenced by the small-world effect.
arXiv comment5 pages, one figure, accepted for publication in Physical Review E
References in corpus (13)
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Evolution of networks
- Ising model in small-world networks
- XY model in small-world networks
- Comment on "Ising model on a small world network"
- Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model
- Introducing Small-World Network Effect to Critical Dynamics
- Solvable Kinetic Gaussian Model in External Field
- Dynamical Decimation Renormalization-Group Technique: Kinetic Gaussian Model on Non-Branching, Braching and Multi-branching Koch Curve
- Kawasaki-type Dynamics: Diffusion in the kinetic Gaussian model
- Generalized Competing Glauber-type Dynamics and Kawasaki-type Dynamics
- Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics