Ising Blockade of Resonant Energy Transport in Dense Spin Ensembles

Abstract

Resonant energy transport in dense, disordered dipolar spin ensembles relaxes far more slowly than predicted by exchange-only theories. We identify the missing mechanism as an Ising blockade: configuration-dependent diagonal interactions dynamically detune neighboring spins, so that the transport bottleneck is set by the correlated pair-detuning $ε_{ij}$ rather than by the single-spin linewidth. The resonant fraction is suppressed linearly with the Ising broadening $Γ_{\mathrm{Ising}}$ -- in contrast to the quadratic suppression of conventional relaxation-time approximations. This single emergent scale yields a fit-free renormalization, $T_r^{\mathrm{corr}} \simeq T_r^{\mathrm{orig}}\,Γ_{\mathrm{Ising}}/σ_{\mathrm{exp}}$, which quantitatively accounts for the anomalous scaling $T_r \propto r^{4.5}$ in three-dimensional superradiant masers. The framework extends naturally across dimensions: geometry-dependent accumulation of Ising fields unifies the 3D exponent with the $T_r\propto r^{3}$ scaling observed in two-dimensional surface spin ensembles.