Effect of long-range interactions on the pure and random quantum Ising transitions

It is well known that the long-range nature of interactions modifies the critical behaviour of classical and quantum systems. In the present article, we discuss some intriguing phenomena related to the phase transition in the pure and random quantum Ising systems in the presence of long-range interactions. We also propose a new model of a quantum Ising system with a ferromagnetic interaction defined on a long-range bond-diluted lattice. Using the results for the one-dimensional long-range bond percolation, we present a phenomenological phase diagram of the one-dimensional dilute model and comment on the higher-dimensional generalisations.