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    Engineering relaxation spectra via feature-conditioned disorder in a transverse-field Ising model

    Mingyang Zhao1,2,3, Hairong Li1,*, Yanshi Zhang2,3,4, Jizheng Duan2,3, Yanwei Chen2,3, Weining Liu1, Zhao Liu1, Baoyu Li1, and Lei Yang2,3,5,†

    • *Contact author: lzulihairong@163.com
    • †Contact author: lyang@impcas.ac.cn

    Phys. Rev. Applied 25, 054006 – Published 4 May, 2026

    DOI: https://doi.org/10.1103/mtz6-fs2n

    Abstract

    We investigate how feature-space dimensionality reshapes relaxation and correlation structure in a transverse-field Ising model with feature-conditioned, ferromagnetically biased bond disorder, analyzed via its anisotropic (two plus one)-dimensional classical counterpart. Using Suzuki–Trotter simulations of the mapped classical system, we study imaginary-time autocorrelators, coarse equal-time spatial summaries, and eigenvalue spectra of equal-time correlation matrices. Each spin is assigned a d-component feature vector, and a similarity scale σ^ controls how feature differences bias the distribution of bond signs. Increasing d homogenizes pairwise feature distances and, together with σ^, tunes bond-sign heterogeneity within this positively biased ensemble. We find a systematic dynamical crossover from short-τ transients at low d to multistep relaxation with long-lived plateaus at higher d, accompanied by a compression of equal-time correlation weight into fewer dominant spatial modes. Feature-conditioned disorder thus provides a controlled framework for studying how correlated disorder reshapes relaxation spectra in disordered Ising networks, with potential relevance to programmable Ising hardware.

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