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arXiv · 2406.13089

Uniqueness and CLT for the Ground State of the Disordered Monomer-Dimer Model on $\mathbb{Z}^{d}$

Kesav Krishnan·Gourab Ray
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Abstract

We prove that the disordered monomer-dimer model does not admit infinite volume incongruent ground states in $\mathbb{Z}^d$ which can be obtained as a limit of finite volume ground states. Furthermore, we also prove that these ground states are stable under perturbation of the weights in a precise sense. As an application, we obtain a CLT for the ground state weight for a growing sequence of tori. Our motivation stems from a similar and long standing open question for the short range Edwards-Anderson spin glass model.

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Kesav Krishnan, Gourab Ray. 2024-06-18. Uniqueness and CLT for the Ground State of the Disordered Monomer-Dimer Model on $\mathbb{Z}^{d}$. https://arxiv.org/abs/2406.13089

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