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

TL;DR

This study explores how quantum fluctuations influence phase transitions in quantum Ising models on small-world networks, revealing that they lower transition temperatures without changing the universality class.

Contribution

It provides a numerical analysis of quantum effects on phase transitions in small-world network-based Ising systems, highlighting the impact of quantum fluctuations on critical behavior.

Findings

Quantum fluctuations do not change the universality class of the phase transition.

Transition temperature decreases with increasing quantum fluctuations.

Critical transverse field $ ext{Δ}_c$ increases with rewiring probability.

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.