We study the effect of long-range connections on the infinite-randomness fixed point associated with the quantum phase transitions in a transverse Ising model (TIM). The TIM resides on a long-range connected lattice where any two sites at a distance $r$ are connected with a nonrandom ferromagnetic bond with a probability that falls algebraically with the distance between the sites as $1∕r^{d+\sigma }$. The interplay of the fluctuations due to dilutions together with the quantum fluctuations due to the transverse field leads to an interesting critical behavior. The exponents at the critical fixed point (which is an infinite randomness fixed point) are related to the classical “long-range” percolation exponents. The most interesting observation is that the gap exponent $\psi$ is exactly obtained for all values of $\sigma$ and $d$. Exponents depend on the range parameter $\sigma$ and show a crossover to short-range values when $\sigma \ge 2-{\eta }_{\mathrm{SR}}$ where ${\eta }_{\mathrm{SR}}$ is the anomalous dimension for the conventional percolation problem. Long-range connections are also found to tune the strength of the Griffiths phase.

• Received 16 August 2006

DOI:https://doi.org/10.1103/PhysRevB.75.052405