Dyson-Ising铁磁体的抽取
Decimation of the Dyson-Ising Ferromagnet
摘要：
我们研究了在相变区（1< $α\leq$ 2，低温）中，具有缓慢衰减的长程对相互作用形式$\frac{1}{{|i-j|}^α}$的一维Dyson-Ising铁磁体的亚晶格的一半位置的抽取。我们证明了在足够低的温度下的抽取措施的非吉布斯性表现出一个点的本质不连续的有限体积条件概率抽取吉布斯措施。因此，结果补充了以前的工作，证明了快速衰减的潜力（$α$ > 2）的吉布斯守恒，并提供了一个“标准”的非吉布斯结果在一维的例子，在静脉中的类似结果在更高的维度为短程模型。我们还讨论了如何这些措施可以适合在一个广义的（几乎与弱）吉布斯框架。此外，我们评论的可能性，类似的结果为其他一些转换。
英文摘要：
We study the decimation to a sublattice of half the sites, of the one-dimensional Dyson-Ising ferromagnet with slowly decaying long-range pair interactions of the form $\frac{1}{{|i-j|}^α}$, in the phase transition region (1< $α\leq$ 2, and low temperature). We prove non-Gibbsianness of the decimated measure at low enough temperatures by exhibiting a point of essential discontinuity for the finite-volume conditional probabilities of decimated Gibbs measures. Thus result complements previous work proving conservation of Gibbsianness for fastly decaying potentials ($α$ > 2) and provides an example of a "standard" non-Gibbsian result in one dimension, in the vein of similar resuts in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations.
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