2025/02/14 by Hideaki Nishikawa, Nishikawa, Hideaki, Keiji Saito +1 · 2 citations
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Machine Learning in Materials Science #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2502.10139
openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as V(r) ∝ 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 ≥ 2, normal diffusion is indicated as long as α> D.