论文标题
1D中的远程模型重新审视
Long-range models in 1D revisited
论文作者
论文摘要
简而言之，我们在远程1D渗透，ISING模型和Potts模型[FS82，NS86，ACCN88，IN88]上重新审视了许多经典结果{S}。更准确地说，我们表明，对于Bernoulli渗透，FK渗透和Potts模型，对于$ 1/r^2 $ - 与大$β$的$ 1/r^2 $ - 互动存在对称性破坏，并且相变一定是不连续的。我们还显示[ACCN88]的表示法表明所有$ q \ geq 1 $ $β^*（q）= 1 $。
In this short note, we revisit a number of classical result{s} on long-range 1D percolation, Ising model and Potts models [FS82, NS86, ACCN88, IN88]. More precisely, we show that for Bernoulli percolation, FK percolation and Potts models, there is symmetry breaking for the $1/r^2$-interaction at large $β$, and that the phase transition is necessarily discontinuous. We also show, following the notation of [ACCN88] that $β^*(q)=1$ for all $q\geq 1$.
