arXiv subjects

Sike Lang

Publications and source records attributed to Sike Lang.

2 recordsLinked to original sources

arXiv2026

The free state for the Potts model on Cayley trees is either extremal or glassy

For the Potts model on the Cayley tree $\mathbb{T}^d$ with branching factor $d\geq 2$, we consider the free state which is obtained as the limiting Gibbs measure with free boundary conditions. We prove that the free state is either extremal or glassy (i.e., whose decomposition into extremal Gibbs measures contains uncountably many components). As a corollary, the free state for the Ising model on $\mathbb{T}^d$ is glassy if and only if the inverse temperature $\beta>\operatorname{arctanh}(1/\sqrt{d})$; this generalizes a previous result by Gandolfo, Maes, Ruiz and Shlosman (2020) from a very low temperature regime to the entire spin-glass regime.

math.PR↗

arXiv2025

Percolation of both signs in a triangular-type 3D Ising model above $T_c$

Let $\mathbb{T}$ be the two-dimensional triangular lattice, and $\mathbb{Z}$ the one-dimensional integer lattice. Let $\mathbb{T}\times \mathbb{Z}$ denote the Cartesian product graph. Consider the Ising model defined on this graph with inverse temperature $\beta$ and external field $h$, and let $\beta_c$ be the critical inverse temperature when $h=0$. We prove that for each $\beta\in[0,\beta_c)$, there exists $h_c(\beta)>0$ such that both a unique infinite $+$cluster and a unique infinite $-$cluster coexist whenever $|h|<h_c(\beta)$. The same coexistence result also holds for the three-dimensional triangular lattice.

math.PR↗