M. E. Fisher, R.E. Hartwig, Adv. Chem. Phys. 15 (1968) 333
Solved in
Percy Deift, Alexander Its, Igor Krasovsky, Asymptotics of Toeplitz, Hankel, and Toeplitz-Hankel determinants with Fisher-Hartwig singularities, Annals of Mathematics 174 (2011), 1243–1299 doi
An older reference about the subject is
Estelle L. Basor, Craig A. Tracy, The Fisher-Hartwig conjecture and generalizations, Physica A 177 (1991) 167-173 doipdf