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 (\(\Gamma_0 \le \Gamma_i \le 2\Gamma_0\)) 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 (\(h=0,\Gamma_0=1\)) there is an infinite disorder quantum fixed point, while at the other end (\(h=2,\Gamma_0=0\)) there is a classical random first-order transition point. Close to this fixed point, for \(h>2\) and \(\Gamma_0>0\) there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.