Energy diffusion in the long-range interacting spin systems

Fuente: arXiv
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Autores principales: Nishikawa, Hideaki, Saito, Keiji
Formato: Preprint
Publicado: 2025
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author Nishikawa, Hideaki
Saito, Keiji
author_facet Nishikawa, Hideaki
Saito, Keiji
contents We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-α}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse Ising model, and the XYZ model in the $D$-dimensional lattice with finite $α>D$ which guarantees the thermodynamic extensivity. In one dimension, both normal and anomalous diffusion are observed, where the anomalous diffusion is attributed to anomalous enhancement of the amplitude of the equilibrium current correlation. We prove the power-law clustering property of arbitrary orders of joint cumulants in general dimensions. Applying this theorem to equal-time current correlations, we further prove several theorems leading to the statement that the sufficient condition for normal diffusion in one dimension is $α> 3/2$ regardless of the models. The fluctuating hydrodynamics approach consistently explains Lévy diffusion for $α< 3/2$, which implies the condition is optimal. In higher dimensions of $D \geq 2$, normal diffusion is indicated as long as $α> D$.
format Preprint
id arxiv_https___arxiv_org_abs_2502_10139
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Energy diffusion in the long-range interacting spin systems
Nishikawa, Hideaki
Saito, Keiji
Statistical Mechanics
Mesoscale and Nanoscale Physics
We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-α}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse Ising model, and the XYZ model in the $D$-dimensional lattice with finite $α>D$ which guarantees the thermodynamic extensivity. In one dimension, both normal and anomalous diffusion are observed, where the anomalous diffusion is attributed to anomalous enhancement of the amplitude of the equilibrium current correlation. We prove the power-law clustering property of arbitrary orders of joint cumulants in general dimensions. Applying this theorem to equal-time current correlations, we further prove several theorems leading to the statement that the sufficient condition for normal diffusion in one dimension is $α> 3/2$ regardless of the models. The fluctuating hydrodynamics approach consistently explains Lévy diffusion for $α< 3/2$, which implies the condition is optimal. In higher dimensions of $D \geq 2$, normal diffusion is indicated as long as $α> D$.
title Energy diffusion in the long-range interacting spin systems
topic Statistical Mechanics
Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2502.10139