Partition function results

3 Sept 2010 PPM's results from:

• Finite Lattice Z(3) models in two and three dimensions (Martin1983):
  • 3-1x6x9-010 (not sure about BC3) - easily done with bc3
  • 3-3x3x9-110 (not sure about BC3)

• Analytic properties of the partition function for statistical mechanical models (Martin1986a)
  • 4-1x4x32-010 (not sure about BC's)
  • 4-1x6x32-010 (not sure about BC's)
  • 4-1x8x24-010 (not sure about BC's)
  • 4-1x10-16-010 (not sure about BC's)
  • 3-1x10x20 (ice model representation)
  • 3-1x8x16 (ice model representation)

My Programs limitations 1 <= q <= 6 For q = 6, what is the largest 2d and 3d model?

• With BC3
  • 6-1x7x7-011 (obviously wrong, produce some error! rerun)

• Without BC3
  • 6-1x9x10-010

For q = 5, what is the largest 2d and 3d model?

• With BC3
  • 5-

• Without BC3
  • 5-03x03x10-110 (In thesis)

For q = 4, what is the largest 2d and 3d model?

• With BC3
  • 4-

• Without BC3
  • 4-01x10x16-010 (this is in thesis temporarily)
  • 4-03x04x10-110 (In thesis!)

For q = 3, what is the largest 2d and 3d model?

• Without BC3
  • 3-1x12x16-010 (In thesis!)
  • 3-4x4x10-110 (In thesis!)
  • Anti ferromagnetic A-3-4x4x10-110 (needs to be put in)

• With BC3
  • 3-1x6x09-011 (In thesis!)

For q = 2, what is the largest 2d and 3d model?

• Without BC3
  • 2-5x5x10-110 (In thesis!)
  • 2-4x6x10-110 (In thesis!)
  • 2-1x16x16-010 (polynomial but no roots)
• With BC3
  • 2-4x4x10-111 (In thesis!)
  • 2-01x13x13-011