The Dimer Constant of the Cubic Lattice
Prior state unknown→proved
a record upper bound; the exact constant remains unknown
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mathematical-physics / Statistical mechanics
The Dimer Constant of the Cubic Lattice
The dimer constant of $\mathbb{Z}^3$, the exponential growth rate of perfect matchings of the cubic lattice, has no closed form and is pinned only by bounds. The upper bound improves from Lundow's $0.457547$, standing since 2001, to $0.452130$, via diagonal transfer layers and an inequality of Csikvari relating the spectral radius of the transfer matrix to the constant.
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The dimer constant of $\mathbb{Z}^3$, the exponential growth rate of perfect matchings of the cubic lattice, has no closed form and is pinned only by bounds. The upper bound improves from Lundow's $0.457547$, standing since 2001, to $0.452130$, via diagonal transfer layers and an inequality of Csikvari relating the spectral radius of the transfer matrix to the constant.
a record upper bound; the exact constant remains unknown
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