Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness

• URL: http://arxiv.org/abs/2603.02308v1
• Date: Mon, 02 Mar 2026 19:00:00 GMT
• Title: Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness
• Authors: Akshat Pandey, Aditya Mahadevan, A. Alan Middleton, Daniel S. Fisher,
• Abstract summary: At low temperatures, the classical two-dimensional random bond Ising model undergoes a frustration-driven ferromagnet-to-paramagnet transition.<n>We show that this critical point can be understood through a renormalization group transformation.
• Score: 0.32226879439224404
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: At low temperatures, the classical two-dimensional random bond Ising model undergoes a frustration-driven ferromagnet-to-paramagnet transition controlled by a zero-temperature fixed point separating ferromagnet and spin glass phases. We show that this critical point can be understood through a renormalization group transformation that constructs the ground state of the Ising model through a sequence of Hamiltonians that, starting with an unfrustrated model, iteratively adds in frustration until the target Hamiltonian is reached. Via a mapping of the thermodynamics of the 2d Ising model to the spectral properties of a related Hermitian matrix -- the Hamiltonian of a noninteracting quantum problem -- this RG procedure corresponds to an iterative diagonalization of the quantum Hamiltonian. The flow toward zero temperature in the Ising picture manifests as a flow toward infinite randomness in the spectrum of the quantum Hamiltonian, with the log gap of the Hamiltonian scaling as a power of the system size: $\log \varepsilon_{\it min}^{-1} \sim L^ψ$. The tunneling exponent $ψ$ is equal to the spin stiffness exponent $θ_c$ characterizing the zero-temperature fixed point.

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