Dynamics of position-disordered Ising spins with a soft-core potential

We theoretically study the magnetization relaxation of Ising spins distributed randomly in a $d$-dimension homogeneous and Gaussian profile under soft-core two-body interaction potential $\ensuremath{\propto}1/[1+{(r/{R}_{c})}^{\ensuremath{\alpha}}]$ $(\ensuremath{\alpha}\ensuremath{\ge}d)$, where $r$ is interspin distance ${R}_{c}$ radius. The dynamics starts with all polarized transverse direction. In case, an analytic expression derived at thermodynamic limit, which as $\ensuremath{\propto}exp(\ensuremath{-}k{t}^{2})$ constant $k$ follows stretched-exponential law long time exponent $\ensuremath{\beta}=d/\ensuremath{\alpha}$. between oscillating behavior observed damping amplitude. For samples, degree disorder system can be controlled by ratio ${l}_{\ensuremath{\rho}}/{R}_{c}$, ${l}_{\ensuremath{\rho}}$ mean investigated numerically. limit ${l}_{\ensuremath{\rho}}/{R}_{c}\ensuremath{\ll}1$, coherent many-body recovered for total despite position spins. opposite ${l}_{\ensuremath{\rho}}/{R}_{c}\ensuremath{\gg}1$, similar that case emerges later after initial fast decay magnetization. obtain stretched $\ensuremath{\beta}\ensuremath{\approx}0.18$ asymptotic evolution $d=3,\ensuremath{\alpha}=6$, different from $(\ensuremath{\beta}=0.5)$.