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arXiv:2607.20036

Vanishing spin stiffness in weakly disordered two-dimensional Heisenberg ferromagnets

Jacopo Niedda, Aldo Coraggio, Giacomo Bracci-Testasecca, Antonello Scardicchio

Published Jul 22, 2026• 0 citations
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Abstract

We show that a small fraction of antiferromagnetic bonds qualitatively alters the long-wavelength dynamics of two-dimensional Heisenberg ferromagnets. Although the classical ground state remains magnetized, weak bond frustration generates logarithmically correlated spatial fluctuations of the local spin stiffness, despite the microscopic disorder being short ranged. A replica field theory calculation shows that the effective disorder strength grows under coarse graining, while the spin stiffness decreases, yielding anomalously soft magnons with a scale-dependent dynamical exponent $z > 2$. Numerical diagonalization of the semiclassical spin-wave Hamiltonian confirms the anomalous low-energy scaling. The flow is toward an infinite-disorder, zero stiffness regime.

DOI
10.48550/arxiv.2607.20036

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We show that a small fraction of antiferromagnetic bonds qualitatively alters the long-wavelength dynamics of two-dimensional Heisenberg ferromagnets. Although the classical ground state remains magnetized, weak bond frustration generates logarithmically correlated spatial fluctuations of the local spin stiffness, despite the microscopic disorder being short ranged. A replica field theory calculation shows that the effective disorder strength grows under coarse graining, while the spin stiffness decreases, yielding anomalously soft magnons with a scale-dependent dynamical exponent z>2z > 2z>2. Numerical diagonalization of the semiclassical spin-wave Hamiltonian confirms the anomalous low-energy scaling. The flow is toward an infinite-disorder, zero stiffness regime.
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The two-dimensional quantum Heisenberg antiferromagnet at zero temperature, with locally frustrating magnetic defects, is studied. We consider two types of defects---an isolated ferromagnetic bond (FMB) and a quantum impurity spin, coupled symmetrically to the two sublattices. A technique is developed to study strong defect-environment interaction. In the case of a FMB we find that, contrary to the previous linear spin-wave result, the local magnetization stays finite even for strong frustration. For an antiferromagnetic coupling of a quantum impurity spin with its environment, we find a local change in the ground state. All our calculations are compared with numerical results from exact diagonalization.
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We investigate quantum phase transitions in the spin-1∕21∕21∕2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating cluster with short ranged antiferromagnetic order. In this phase, the low-temperature uniform susceptibility diverges algebraically with non-universal exponents. This is a signature that the quantum-disordered phase is a quantum Griffiths phase, as also directly confirmed by the statistical distribution of local gaps. This study thus presents evidence of a genuine quantum Griffiths phenomenon in a two-dimensional Heisenberg antiferromagnet.
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By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the S = 1 antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at δ Δ ∼ 0.5 with more and more low-energy excitations coming out. After the critical disorder strength δ c ∼ 1, the system reaches a random-singlet phase with prominent sharp peak at ω = 0 and broad continuum at ω > 0 of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These “spins” can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at ω = 0.