Locally free group as a bridge between combinatorics of heaps and statistics of spin systemsReport as inadecuate



 Locally free group as a bridge between combinatorics of heaps and statistics of spin systems


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We demonstrate that the locally free group is, on the one hand, a powerful tool for the enumerative combinatorics of heaps of pieces and, on the other hand, a natural parametrization of some two-dimensional lattice spin systems. On the example of the 1+1-dimensional directed lattice animals on a strip with a fixed set of roots we show how the locally free group can be used for a simple statistical derivation of the corresponding partition function. We discuss how our approach is connected to other known geometrical methods, like the -inversion lemma-. Analyzing the algebraic structure of the locally free group, we find its link to a -matrix ansatz- used in the solution of 1-dimensional asymmetric simple exclusion models.



Author: Nils Haug; Sergei Nechaev

Source: https://archive.org/



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