The onset of spin glass freezing in dilute Ising systems with long range interactions is investigated within the framework of a random local field approach (previously developed for disordered ferromagnets and ferroelectrics) with the use of numerical simulations. The problem reduces to the diagonalization of an N×N random matrix, N being the number of spins in the simulation, whose elements depend on the spin–spin interaction and temperature. We identify the onset of spin glass freezing with the temperature at which this boundary eigenvalue separating localized and extended states is equal to one. Numerical simulations give a reasonable value of the freezing temperature for dilute RKKY spin glasses and reproduce its linear concentration dependence in agreement with the scaling relation.
Abstract One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.