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Weak disorder in the stochastic mean-field model of distance II
First passage percolation complete graph extreme value theory hopcount
2010/12/9
In this paper, we study the complete graph Kn with n vertices, where we attach an i.i.d. weight to each of the n(n − 1)/2 edges. We focus on the weight Wn and the number of edges Hn of the minim...
On Random Field Induced Ordering in the Classical XY Model
Random Field Induced Ordering Classical XY Model
2010/12/13
Consider the classical XY model in a weak random external field pointing along the Y axis with strength . We study the behavior of this model as the range of the interaction is varied.
We prove that...