KTH/Nordita/SU seminar in Theoretical Physics
Critical percolation and qKZ equations
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Europe/Stockholm
FA31
FA31
Description
Based on the work of Razumov and Stroganov it was noted that many exact
expressions for certain correlation functions for critical bond
percolation could be found for arbitrary system sizes and distances
involved. These results were obtained by the study of the
Perron-Frobenius eigenvector of the transfer matrix for the cylinder or
strip. It turned out far more difficult to obtain similar results for
site percolation model on the triangular lattice.
Here we present an approach to both site- and bond percolation, applicable to arbitrary rhombus tilings and to isoradial lattices respectively. It makes use of relations known as q-Knizhnik-Zamolodchikov equations (qKZ). These relations are satisfied by the correlations in the models. In some geometries these equations can be solved, yielding the correlation functions. For some specific correlation functions, these results can be extrapolated to arbitrary sizes.
Here we present an approach to both site- and bond percolation, applicable to arbitrary rhombus tilings and to isoradial lattices respectively. It makes use of relations known as q-Knizhnik-Zamolodchikov equations (qKZ). These relations are satisfied by the correlations in the models. In some geometries these equations can be solved, yielding the correlation functions. For some specific correlation functions, these results can be extrapolated to arbitrary sizes.