Dynamics of position disordered Ising spins with a soft-core potential
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 radi...
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| Main Authors: | , , , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
November 2, 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-7 |
| Online Access: | Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2111.00779
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| Author Notes: | Canzhu Tan, Xiaodong Lin, Yabing Zhou, Y.H. Jiang, Matthias Weidemüller, and Bing Zhu |
| Summary: | 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 ($\beta=0.5$). |
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| Item Description: | Gesehen am 14.12.2021 |
| Physical Description: | Online Resource |