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In this paper, we consider nearest-neighbor oriented percolation with independent Bernoulli bond-occupation probability on the $d$-dimensional body-centered cubic (BCC) lattice $mathbb{L}^d$ and the set of non-negative integers $mathbb{Z}_+$. Thanks to the nice structure of the BCC lattice, we prove that the infrared bound holds on $mathbb{L}^dtimesmathbb{Z}_+$ in all dimensions $dgeq 9$. As opposed to ordinary percolation, we have to deal with the complex numbers due to asymmetry induced by time-orientation, which makes it hard to estimate the bootstrapping functions in the lace-expansion analysis from above. By investigating the Fourier-Laplace transform of the random-walk Green function and the two-point function, we drive the key properties to obtain the upper bounds and resolve a problematic issue in Nguyen and Yangs bound.
We discuss spin models on complete graphs in the mean-field (infinite-vertex) limit, especially the classical XY model, the Toy model of the Higgs sector, and related generalizations. We present a number of results coming from the theory of large dev
The aim of this survey is to explain, in a self-contained and relatively beginner-friendly manner, the lace expansion for the nearest-neighbor models of self-avoiding walk and percolation that converges in all dimensions above 6 and 9, respectively.
This article will review recent results on dimensional reduction for branched polymers, and discuss implications for critical phenomena. Parisi and Sourlas argued in 1981 that branched polymers fall into the universality class of the Yang-Lee edge in
We previously reported on a recursive method to generate the expansion of the lattice Green function of the $d$-dimensional face-centred cubic lattice (fcc). The method was used to generate many coefficients for d=7 and the corresponding linear diffe
We investigate the influence of the range of interactions in the two-dimensional bond percolation model, by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges, as expressed by the number $z$ of equivalent