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 language||English (US)|
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|State||Published - Aug 2004|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty