Asymptotic Behavior of Spanning Forests and Connected Spanning Subgraphs on Two-Dimensional Lattices

Exponential Growth Constants for Spanning Forests on Archimedean Lattices: Values and Comparisons of Upper Bounds

We compare our upper bounds on the exponential growth constant $ϕ(Λ)$ characterizing the asymptotic behavior of spanning forests on Archimedean lattices $Λ$ with recently derived upper bounds. Our upper bounds on $ϕ(Λ)$, which are very close to the respective values of $ϕ(Λ)$ that we have calculated, are shown to be significantly better for these lattices than the new upper bounds.

通过随机生成树进行谱熵计算

Spectral Entropy via Random Spanning Forests

本文提出通过随机生成树进行谱熵计算的方法，利用Wilson采样避免了特征分解，实现了高效估计配分函数和熵。

Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions

We present Monte Carlo simulations of the spanning-forest model (q \to 0 limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show that, in contrast to the two-dimensional case, the model has a "ferromagnetic" second-order phase transition at a finite positive value w_c. We present numerical estimates of w_c and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.

Spanning Forests on Random Planar Lattices

The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q -> 0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model in the limit n -> -1, the expansion parameter t counting the number of components in the forest. We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k = 3, a correspondence is found with the Kostov solution of the loop-…