Correlation Functions of the Transverse Ising Chain at the Critical Field for Large Temporal and Spatial Separations

McCoy, Barry M.; Perk, Jacques H.H.; Shrock, Robert E.

doi:10.1016/0550-3213(83)90041-X

Correlation Functions of the Transverse Ising Chain at the Critical Field for Large Temporal and Spatial Separations

Barry M. McCoy
(
- SUNY, Stony Brook
)
,
Jacques H.H. Perk
(
- SUNY, Stony Brook
)
,
Robert E. Shrock
(
- SUNY, Stony Brook
)

Mar, 1983

14 pages

Published in:

Nucl.Phys.B 220 (1983) 269-282

Published: 1983

DOI:

10.1016/0550-3213(83)90041-X

Report number:

ITP-SB-83-5

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Abstract: (Elsevier)

We study the behavior of 〈 σ 0 x ( t ) σ n x (0)〉 and 〈 σ 0 y ( t ) σ n y (0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with 0 ⩽ n t <1 , 1 < n t , or t = n + n 1 3 ( z 2 ) where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.