标题： 半无限伊辛模型中的相变与衰减场 显示英文标题

标题： Phase Transitions in the semi-infinite Ising model with a decaying field

摘要： 我们研究带有外场$h_i = \lambda |i_d|^{-\delta}$的半无限 Ising 模型，$\lambda$是壁的影响，$\delta>0$。这个外场随着远离壁而衰减。 我们能够证明，当$\delta>1$和$\beta > \beta_c(d)$时，存在一个临界值$0< \lambda_c:=\lambda_c(\delta,\beta)$，使得对于$\lambda<\lambda_c$存在相变，而对于$\lambda>\lambda_c$我们有吉布斯态的唯一性。 此外，当 $\delta<1$，对于任何正的 $\beta$ 和 $\lambda$，我们只有一个吉布斯态。 显示英文摘要

摘要： We study the semi-infinite Ising model with an external field $h_i = \lambda |i_d|^{-\delta}$, $\lambda$ is the wall influence, and $\delta>0$. This external field decays as it gets further away from the wall. We are able to show that when $\delta>1$ and $\beta > \beta_c(d)$, there exists a critical value $0< \lambda_c:=\lambda_c(\delta,\beta)$ such that, for $\lambda<\lambda_c$ there is phase transition and for $\lambda>\lambda_c$ we have uniqueness of the Gibbs state. In addition, when $\delta<1$, we have only one Gibbs state for any positive $\beta$ and $\lambda$.