Dynamics of position disordered Ising spins with a soft-core potential
| Autor: | Tan, Canzhu, Lin, Xiaodong, Zhou, Yabing, Jiang, Y. H., Weidemüller, Matthias, Zhu, Bing |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.105.104204 |
| Popis: | We theoretically study magnetization relaxation of Ising spins distributed randomly in a $d$-dimension homogeneous and Gaussian profile under a soft-core two-body interaction potential $\propto1/[1+(r/R_c)^\alpha]$ ($\alpha\ge d$), where $r$ is the inter-spin distance and $R_c$ is the soft-core radius. The dynamics starts with all spins polarized in the transverse direction. In the homogeneous case, an analytic expression is derived at the thermodynamic limit, which starts as $\propto\exp(-t^2)$ and follows a stretched-exponential law asymptotically at long time with an exponent $\beta=d/\alpha$. In between an oscillating behaviour is observed with a damping amplitude. For Gaussian samples, the degree of disorder in the system can be controlled by the ratio $l_\rho/R_c$ with $l_\rho$ the mean inter-spin distance and the magnetization dynamics is investigated numerically. In the limit of $l_\rho/R_c\ll1$, a coherent many-body dynamics is recovered for the total magnetization despite of the position disorder of spins. In the opposite limit of $l_\rho/R_c\gg1$, a similar dynamics as that in the homogeneous case emerges at later time after a initial fast decay of the magnetization. We obtain a stretched exponent of $\beta\approx0.18$ for the asymptotic evolution with $d=3, \alpha=6$, which is different from that in the homogeneous case ($\beta=0.5$). Comment: 7 pages, 5 figures, comments welcome |
| Databáze: | arXiv |
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