High-temperature criticality in power-law interacting spin systems

We study the phase transition of a d-dimensional XY model with power-law interactions ($1/r^{alpha}$), which can describe interactions in trapped-ion spin systems, Rydberg atoms, polar molecules, and magnetic atoms, as a function of the magnetic field $h$ along the $z$ direction and the temperature. Elementary magnetic excitations in the system (magnons) correspond to spin flips that propagate with dispersion $xi_{mathbf{k}}propto |mathbf{k}|^{alpha-d}$. Using the renormalization group approach, we demonstrate that the system exhibits a phase transition between weakly and strongly interacting phases. In the former, the system behaves as a gas of weakly interacting magnons. In the latter, low-energy magnetic excitations are strongly interacting. The phase transition can be triggered by increasing temperature or decreasing the magnetic field $h$. One can probe such transition by measuring the relaxation time of the magnetization. This transition is similar to the disorder-driven phase transitions in systems with power-law quasiparticle dispersion $xi_{mathbf{k}}propto |mathbf{k}|^{alpha-d}$ (e.g. three-dimensional Weyl and Dirac materials, cold-atom systems with long-range interactions).