Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

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

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
, Jacques H.H. Perk
, Robert E. Shrock

Institute for Theoretical Physics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

105 Scopus citations

Abstract

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is 1 2Σ_l{σ_l^xσ_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.

Original language	English
Pages (from-to)	35-47
Number of pages	13
Journal	Nuclear Physics, Section B
Volume	220
Issue number	1
DOIs	https://doi.org/10.1016/0550-3213(83)90132-3
State	Published - May 16 1983

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title = "Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field",

abstract = "We study the correlation function 〈σ0x(t)σnx(0)〉 of the transverse Ising model in a critical field whose hamiltonian is 1 2Σl\{σlxσl+1x-σlz\}. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlev{\'e} 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.",

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AU - McCoy, Barry M.

AU - Perk, Jacques H.H.

AU - Shrock, Robert E.

PY - 1983/5/16

Y1 - 1983/5/16

N2 - We study the correlation function 〈σ0x(t)σnx(0)〉 of the transverse Ising model in a critical field whose hamiltonian is 1 2Σl{σlxσl+1x-σlz}. 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.

AB - We study the correlation function 〈σ0x(t)σnx(0)〉 of the transverse Ising model in a critical field whose hamiltonian is 1 2Σl{σlxσl+1x-σlz}. 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.

UR - https://www.scopus.com/pages/publications/0003088318

U2 - 10.1016/0550-3213(83)90132-3

DO - 10.1016/0550-3213(83)90132-3

M3 - Article

AN - SCOPUS:0003088318

SN - 0550-3213

VL - 220

SP - 35

EP - 47

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

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