Discrete Scale Invariance of Ising Mesons
Abstract
Discrete scale invariance often arises from resonant few-body or singular scale-invariant dynamics. We show that it can instead emerge in the internal motion of a composite excitation in an ordered quantum magnet. In the marginal 1/r4 transverse-field Ising chain, long-range bonds generate an asymptotic inverse-square attraction between dressed domain walls, with strength fixed by the spontaneous magnetization. The dressed two-kink threshold curvature sets the relative kinetic scale. Together, these independently accessible quantities determine the scale-anomaly exponent and hence the meson hierarchy. In the supercritical regime, the same exponent governs geometric binding-energy and size ratios, logarithmic level accumulation, and log-periodic threshold scattering. Full-spin exact diagonalization and a fourth-order weak-field Hamiltonian support the coupled energy--size scaling in the finite window between core and ring effects. This provides a microscopic many-body realization of quantum limit-cycle physics, with its universal scaling fixed by magnetic order and kink mobility.
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BibTeX
@misc{vasilyev2026discrete,
title = {{Discrete Scale Invariance of Ising Mesons}},
author = {Denis V. Vasilyev and Abbas Ali Saberi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35940},
eprint = {2609.35940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35940},
}
RIS
TY - UNPB
TI - Discrete Scale Invariance of Ising Mesons
AU - Denis V. Vasilyev
AU - Abbas Ali Saberi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35940
UR - https://arxiv.org/abs/2609.35940
AB - Discrete scale invariance often arises from resonant few-body or singular scale-invariant dynamics. We show that it can instead emerge in the internal motion of a composite excitation in an ordered quantum magnet. In the marginal 1/r^4 transverse-field Ising chain, long-range bonds generate an asymptotic inverse-square attraction between dressed domain walls, with strength fixed by the spontaneous magnetization. The dressed two-kink threshold curvature sets the relative kinetic scale. Together, these independently accessible quantities determine the scale-anomaly exponent and hence the meson hierarchy. In the supercritical regime, the same exponent governs geometric binding-energy and size ratios, logarithmic level accumulation, and log-periodic threshold scattering. Full-spin exact diagonalization and a fourth-order weak-field Hamiltonian support the coupled energy--size scaling in the finite window between core and ring effects. This provides a microscopic many-body realization of quantum limit-cycle physics, with its universal scaling fixed by magnetic order and kink mobility.
ER -