Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field |
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Authors: | Barry M. McCoy Jacques H.H. Perk Robert E. Shrock |
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Affiliation: | 1. Institute for Theoretical Physics, State University of New York, Stony Brook, Long Island, New York 11794, USA |
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Abstract: | We study the correlation function 〈σ0x(t)σnx(0)〉 of the transverse Ising model in a critical field whose hamiltonian is . 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. |
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