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

• URL: http://arxiv.org/abs/2111.00779v1
• Date: Mon, 1 Nov 2021 09:16:39 GMT
• Title: Dynamics of position disordered Ising spins with a soft-core potential
• Authors: Canzhu Tan, Xiaodong Lin, Yabing Zhou, Y. H. Jiang, Matthias Weidem\"uller, Bing Zhu
• Abstract summary: We study magnetization relaxation of Ising spins distributed randomly in a $d$-dimension. In the homogeneous case, an analytic expression is derived at the thermodynamic limit. In the opposite limit of $l_rho/R_cgg1$, a similar dynamics emerges at later time.
• Score: 4.243439940856083
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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