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Status |
Confirmed |
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Seminar Series |
SEM-LPTMC |
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Subjects |
cond-mat.mes-hall |
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Date |
Monday 16 September 2019 |
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Time |
10:45 |
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Institute |
LPTMC |
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Seminar Room |
Jussieu, tower 13-12, room 5-23 |
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Speaker's Last Name |
Dornic |
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Speaker's First Name |
Ivan |
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Speaker's Email Address |
ivan [dot] dornic [at] cea [dot] fr |
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Speaker's Institution |
SPEC CEA Saclay & LPTMC |
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Title |
A tale of Pfaffian persistence tails told by a Painlevé VI transcendent |
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Abstract |
We identify the persistence probability for the spin located at the origin of a half-space magnetized
Glauber-Ising chain as a Fredholm Pfaffian gap probability generating function with a sech-kernel. This is
then recast as a tau-function for a certain Painlevé VI transcendent - a sort of exact Kramers' formula for
the associated explicitely time-dependent Hamiltonian - where the persistence exponent emerges as an
asymptotic decay rate. By a known yet remarkable correspondence that relates Painlevé equations to
Bonnet surfaces, the persistence probability has also a geometric meaning à la Gauss-Bonnet in terms of
the intrinsic curvature of the underlying surface. Since the same sech-kernel with an underlying Pfaffian
structure shows up in a variety of Gaussian first-passage problems, our Painlevé VI characterization
appears as a universal probability distribution akin to the famous Painlevé II Tracy-Widom laws. Its tail
behavior in the magnetization-symmetric case allows in particular to recover the exact value 3/16 for the
persistence exponent of a 2d diffusing random field, as found very recently by Poplavskyi and Schehr
(arXiv:1806.11275). Due to its topological origin, this value should constitute the super-universal
persistence exponent for the coarsening of a non-conserved scalar order parameter in two space
dimensions. |
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