The Entropy of Dimer or Monomer-Dimer Systems on Lattices


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  • Speaker: Professor Emeritus Paul Federbush (U-M Mathematics)
  • Host Department: Physics
  • Date: 10/15/2013
  • Time: 4:00 PM - 5:00 PM

  • Location: 335 West Hall

  • Description:

    How many ways are there of covering a chess board with dominoes (the dimer problem) or covering a fraction p of the squares (the monomer-dimer problem). Dominoes cover two neighboring squares, and must not overlap. This easily generalizes to the same questions on arbitrary lattices in any dimension. We discuss results (mostly very new) , proved, numerical, conjectured, particularly for d-dimensional rectangular lattices. There is a wonderful conjecture. Certainly no familiarity with dimer problems is assumed.