论文标题
旋转玻璃的自由能扩展具有有限连接的$ \ infty $ rsb
Free energy expansion of the spin glass with finite connectivity for $\infty$ RSB
论文作者
论文摘要
在本文中，我们研究了有限的连通性旋转玻璃问题。我们的工作集中在具有Poissonian分布式连接的图上的自旋玻璃自由能的无限连接点的扩展：我们有兴趣研究大值或连接性$ z $的无限连接结果的一阶校正。在先前的工作中，对一个和两个复制对称性断裂进行了相同的计算。一阶校正的结果在零温度的极限下发散，建议它是具有有限数量的复制对称性断裂的伪像。在本文中，我们能够计算出无限数量的复制对称性破坏的扩展：在零温度极限中，我们获得了一个定义的自由能。我们已经表明，在无限数量的复制对称性破裂的情况下，取消术语发生了，并且扩展的病理行为仅是由于副本对称性破裂的有限数量。
In this paper, we investigate the finite connectivity spin-glass problem. Our work is focused on the expansion around the point of infinite connectivity of the free energy of a spin glass on a graph with Poissonian distributed connectivity: we are interested to study the first-order correction to the infinite connectivity result for large values or the connectivity $z$. The same calculations for one and two replica symmetry breakings were done in previous works; the result for the first-order correction was divergent in the limit of zero temperature and it was suggested that it was an artifact for having a finite number of replica symmetry breakings. In this paper we are able to calculate the expansion for an infinite number of replica symmetry breakings: in the zero-temperature limit, we obtain a well defined free energy. We have shown that cancellations of divergent terms occur in the case of an infinite number of replica symmetry breakings and that the pathological behavior of the expansion was due only to the finite number of replica symmetry breakings.
