A refined Razumov-Stroganov conjecture

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Abstract

We extend the Razumov-Stroganov conjecture relating the groundstate of the O(1) spin chain to alternating sign matrices by relating the groundstate of the monodromy matrix of the O(1) model to the so-called refined alternating sign matrices, i.e. with prescribed configuration of their first row, as well as to refined fully-packed loop configurations on a square grid, keeping track both of the loop connectivity and of the configuration of their top row. We also conjecture a direct relation between this groundstate and refined totally symmetric self-complementary plane partitions, namely, in their formulation as sets of non-intersecting lattice paths, with the prescribed last steps of all paths.

Original languageEnglish (US)
Article numberP08009
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number8
DOIs
StatePublished - Aug 2004
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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