Time Dependent Correlation Functions of the Transverse Ising Chain at the Critical Magnetic Field

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

doi:10.1016/0550-3213(83)90132-3

Time Dependent Correlation Functions of the Transverse Ising Chain at the Critical Magnetic Field

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

Nov, 1982

13 pages

Published in:

Nucl.Phys.B 220 (1983) 35-47

Published: 1983

DOI:

10.1016/0550-3213(83)90132-3

Report number:

ITP-SB-82-49

View in:

AMS MathSciNet

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Abstract: (Elsevier)

We study the correlation function 〈 σ 0 x ( t ) σ n x (0)〉 of the transverse Ising model in a critical field whose hamiltonian is 1 2 Σ l {σ l x σ l+1 x −σ l z } . At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n . The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.

STATISTICAL MECHANICS: ISING
SPIN: CORRELATION FUNCTION
CORRELATION FUNCTION: SPIN
STATISTICAL MECHANICS: CRITICAL PHENOMENA
BOUNDARY CONDITION
TRANSFORMATION: ASYMPTOTIC BEHAVIOR
NUMERICAL CALCULATIONS