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SUMMARY:High-density hard-core configurations on a triangular lattice - Yu
ri Suhov (Penn State and Cambridge)
DTSTART;VALUE=DATE-TIME:20180601T110000Z
DTEND;VALUE=DATE-TIME:20180601T120000Z
UID:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
DESCRIPTION:The high-density hard-core configuration model has attracted a
ttention for quite a long time. The first rigorous results about the phase
transition on a lattice with a nearest-neighbor exclusion where published
by Dobrushin in 1968. In 1979\, Baxter calculated the free energy and spe
cified the critical point on a triangular lattice with a nearest-neighbor
exclusion\; in 1980 Andrews gave a rigorous proof of Baxter's calculation
with the help of Ramanujan's identities. On a square lattice the nearest-n
eighbor exclusion critical point has been estimated from above and below i
n a series by a number of authors.\n\nWe analyze the hard-core model on a
triangular lattice and identify the extreme Gibbs measures (pure phases) f
or high densities. Depending on arithmetic properties of the hard-core dia
meter $D$\, the number of pure phases equals either $D^2$ or $2D^2$. A cla
ssification of possible cases can be given in terms of Eisenstein primes.\
n\nIf the time allows\, I will mention 3D analogs of some of these results
.\n\nThis is a joint work with A Mazel and I Stuhl\; cf. arXiv:1803.04041.
No special knowledge will be assumed from the audience.\n\n\nSpeakers:\nY
uri Suhov (Penn State and Cambridge)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
URL:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
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DESCRIPTION:Talk:High-density hard-core configurations on a triangular lat
tice - Yuri Suhov (Penn State and Cambridge)
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