Reentrant Random Quantum Ising Antiferromagnet

We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1\le J_i\le 2)$ and uniformly distributed random transverse fields (${\mathrm{\Gamma }}_0\le {\mathrm{\Gamma }}_i\le 2{\mathrm{\Gamma }}_0$) in the presence of a homogeneous longitudinal field, $h$. Using different numerical techniques (DMRG, combinatorial optimisation and strong disorder RG methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line ($h=0,{\mathrm{\Gamma }}_0=1$) there is an infinite disorder quantum fixed point, while at the other end ($h=2,{\mathrm{\Gamma }}_0=0$) there is a classical random first-order transition point. Close to this fixed point, for $h>2$ and ${\mathrm{\Gamma }}_0>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.