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

• Verfasst von: Tan, Canzhu [VerfasserIn]
• Verfasst von: Lin, Xiaodong [VerfasserIn]
• Verfasst von: Zhou, Yabing [VerfasserIn]
• Verfasst von: Jiang, Yuhai [VerfasserIn]
• Verfasst von: Weidemüller, Matthias [VerfasserIn]
• Verfasst von: Zhu, Bing [VerfasserIn]
• Titel: Dynamics of position disordered Ising spins with a soft-core potential
• Verf.angabe: Canzhu Tan, Xiaodong Lin, Yabing Zhou, Y.H. Jiang, Matthias Weidemüller, and Bing Zhu
• E-Jahr: 2021
• Jahr: November 2, 2021
• Umfang: 7 S.
• Fussnoten: Gesehen am 14.12.2021
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2111.00779, Seite 1-7
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Condensed Matter - Disordered Systems and Neural Networks
• Sach-SW: Condensed Matter - Statistical Mechanics
• Sach-SW: Physics - Atomic Physics
• Sach-SW: Quantum Physics
• K10plus-PPN: 1782088040

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 ($\beta=0.5$).