Comment on "Ising model on a small world network"

Abstract

In the recent study of the Ising model on a small-world network by A. Pȩkalski [Phys. Rev. E {\bf 64}, 057104 (2001)], a surprisingly small value of the critical exponent $\beta \approx 0.0001$ has been obtained for the temperature dependence of the magnetization. We perform extensive Monte Carlo simulations of the same model and conclude, via the standard finite-size scaling of various quantities,that the phase transition in the model is of the mean-field nature, in contrast to the work by A. Pȩkalski but in accord with other existing studies.

to be published in PRE

References in corpus (2)

• XY model in small-world networks
• Relaxational dynamics study of the classical Heisenberg spin XY model in spherical coordinate representation

Cited by in corpus (50)

• The structure and function of complex networks
• Critical phenomena in complex networks
• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Nonequilibrium transitions in complex networks: a model of social interaction
• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Finite-size scaling in complex networks
• Critical phenomena in networks
• Performance of networks of artificial neurons: The role of clustering
• Disorder induced phase transition in kinetic models of opinion dynamics
• Potts model on complex networks
• Dynamic critical behavior of the XY model in small-world networks
• Interface Motion and Pinning in Small World Networks
• Exact Solution of Ising Model on a Small-World Network
• Testing the Collective Properties of Small-World Networks through Roughness Scaling
• Scaling in Small-World Resistor Networks
• Dynamic Transitions in Small World Networks: Approach to Equilibrium
• Curvature-induced frustration in the $XY$ model on hyperbolic surfaces
• Synchronization Landscapes in Small-World-Connected Computer Networks
• Phase transition in the Ising model on a small-world network with distance-dependent interactions
• Quantum and classical diffusion in small-world networks
• Social phase transition in Solomon network
• Phase Transition of XY Model in Heptagonal Lattice
• Phase transitions in Ising model on a Euclidean network
• Instability of defensive alliances in the predator-prey model on complex networks
• Asymmetrically coupled directed percolation systems
• Extreme fluctuations in noisy task-completion landscapes on scale-free networks
• Is small-world network disordered?
• Irreversible growth of binary mixtures on small-world networks
• Majority-vote model on spatially embedded networks: crossover from mean-field to Ising universality classes
• Phase Synchronization of non-Abelian Oscillators on Small-World Networks
• In search for the social hysteresis -- the symmetrical threshold model with independence on Watts-Strogatz graphs
• Random field Ising model on networks with inhomogeneous connections
• Ising model on a 2D additive Small-World Network
• Critical Phenomena and Strategy Ordering with Hub Centrality Approach in the Aspiration-based Coordination Game
• Slow relaxation in the Ising model on a small-world network with strong long-range interactions
• A small-world search for quantum speedup: How small-world interactions can lead to improved quantum annealer designs
• Magnetic models on various topologies
• Non-equilibrium Ising Model on a 2D Additive Small-World Network
• Susceptible-Infected-Recovered model on Euclidean network
• Phase transition of a one-dimensional Ising model with distance-dependent connections
• Reentrant phase transition in a predator-prey model
• Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures
• Magnetic Small World Nanomaterials: Physical Small World Networks
• Effects of substrate network topologies on competition dynamics
• Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics
• One-dimensional Ising model built on small-world networks: competing dynamics
• Synchronization in Small-World-Connected Computer Networks
• Quantum magnetism on small-world networks
• Curie Temperature for Small World Ising Systems of Different Dimensions
• The free and freer XY models