一维随机能量模型中的镶嵌长度和有限相互作用范围效应
Mosaic length and finite interaction-range effects in a one dimensional random energy model
摘要：
在本文中，我们研究有限的相互作用范围的修正马赛克图片的玻璃化转变出现的大相互作用范围的无序模型的Kac极限的研究。为此目的，我们考虑在一个一维随机能量模型中设置关联函数或重叠作为相互作用范围的函数。在Kac极限中，镶嵌长度定义了将高重叠相位与低重叠相位分离的尖锐的一阶过渡。相应地，我们发现重叠曲线作为窗口大小和不同的有限相互作用范围的函数大致在镶嵌长度处相交。尽管如此，我们发现非常缓慢的收敛到Kac限制，我们讨论为什么这可能是一个问题，在现实的模型中测量的马赛克长度。
英文摘要：
In this paper we study finite interaction range corrections to the mosaic picture of the glass transition as emerges from the study of the Kac limit of large interaction range for disordered models. To this aim we consider point to set correlation functions, or overlaps, in a one dimensional random energy model as a function of the range of interaction. In the Kac limit, the mosaic length defines a sharp first order transition separating a high overlap phase from a low overlap one. Correspondingly we find that overlap curves as a function of the window size and different finite interaction ranges cross roughly at the mosaic lenght. Nonetheless we find very slow convergence to the Kac limit and we discuss why this could be a problem for measuring the mosaic lenght in realistic models.
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