LAUSR

We compute the transition asymptotics (double-scaling limits) of Toeplitz determinants generated by symbols ft possessing Fisher-Hartwig singularities. The symbols ft that we consider depend on a parameter t such that ft has one Fisher-Hartwig singularity when t > 0 and two Fisher-Hartwig singularities when t = 0. Unlike in the other studies of the transition asymptotics of Toeplitz determinants, our setting involves the emergence of Fisher-Hartwig representations as t → 0. We use the Riemann-Hilbert problem for orthogonal polynomials and its connection to Painlevé transcendents to obtain the asymptotics. We apply our results to study a special correlator known as the emptiness formation probability (EFP) for the one-dimensional anisotropic XY spin1/2 chain in a transverse magnetic field, and describe its transition between different regions in the phase diagram across critical lines.