Jian Ding

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math.PR2025

Non-ergodicity for the noisy majority vote process on trees

Jian Ding, Fenglin Huang

We consider the noisy majority vote process on infinite regular trees with degree $d \geq 3$ , and we prove the non-ergodicity, i.e., there exist multiple equilibrium measures. Our w…

math.PR2025

Phase transitions in low-dimensional long-range random field Ising models

Jian Ding, Fenglin Huang, João Maia

We consider the long-range random field Ising model in dimension $d = 1, 2$ , whereas the long-range interaction is of the form $J_{x y} = ∣ x - y ∣^{- α}$ with $1 < α < 3/2$ for $d = 1$ and…

math.PR2023

A phase transition and critical phenomenon for the two-dimensional random field Ising model

Jian Ding, Fenglin Huang, Aoteng Xia

We study the random field Ising model in a two-dimensional box with side length $N$ where the external field is given by independent normal variables with mean $0$ and variance $ε^…