Effect of Quantum Fluctuations in an Ising System on Small-World Networks

Abstract

We study quantum Ising spins placed on small-world networks. A simple model is considered in which the coupling between any given pair of spins is a nonzero constant if they are linked in the small-world network and zero otherwise. By applying a transverse magnetic field, we have investigated the effect of quantum fluctuations. Our numerical analysis shows that the quantum fluctuations do not alter the universality class at the ferromagnetic phase transition, which is of the mean-field type. The transition temperature is reduced by the quantum fluctuations and eventually vanishes at the critical transverse field ${\Delta }_c$. With increasing rewiring probability, ${\Delta }_c$ is shown to be enhanced.

5 pages, 5 figures

References in corpus (4)

• Synchronization in small-world systems
• Ising model in small-world networks
• Spontaneous structure formation in a network of chaotic units with variable connection strengths
• XY model in small-world networks

Cited by in corpus (5)

• Quantum critical behavior of the quantum Ising model on fractal lattices
• Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures
• Quantum phase transition of the transverse-field quantum Ising model on scale-free networks
• Potts model with q=3 and 4 states on directed Small-World network
• Quantum magnetism on small-world networks