215 research outputs found
Fisher-Hartwig conjecture and the correlators in XY spin chain
We apply the theorems from the theory of Toeplitz determinants to calculate
the asymptotics of the correlators in the XY spin chain in the transverse
magnetic field. The asymptotics of the correlators for the XX spin chain in the
magnetic field are obtained.Comment: LaTex, 10 page
Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices
Distribution functions for random variables that depend on a parameter are
computed asymptotically for ensembles of positive Hermitian matrices. The
inverse Fourier transform of the distribution is shown to be a Fredholm
determinant of a certain operator that is an analogue of a Wiener-Hopf
operator. The asymptotic formula shows that up to the terms of order ,
the distributions are Gaussian
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