article published yes László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Diamagnetism of the magnetic Schrödinger operator and paramagnetism of the Pauli operator are rigorously proven for nonhomogeneous magnetic fields in the large field, in the large temperature and in the semiclassical asymptotic regimes. New counterexamples are presented which show that neither dia-nor paramagnetism is true in a robust sense (without asymptotics). In particular, we demonstrate that the recent diamagnetic comparison result by Loss and Thaller [M. Loss and B. Thaller, Commun. Math. Phys. (submitted)] is essentially the best one can hope for. American Institute of Physics1997 eng 0022-248810.1063/1.531909 3831289 - 1317 yes Erdös, László. “Dia- and Paramagnetism for Nonhomogeneous Magnetic Fields.” <i>Journal of Mathematical Physics</i>, vol. 38, no. 3, American Institute of Physics, 1997, pp. 1289–317, doi:<a href="https://doi.org/10.1063/1.531909">10.1063/1.531909</a>. L. Erdös, “Dia- and paramagnetism for nonhomogeneous magnetic fields,” <i>Journal of Mathematical Physics</i>, vol. 38, no. 3. American Institute of Physics, pp. 1289–1317, 1997. Erdös L. Dia- and paramagnetism for nonhomogeneous magnetic fields. <i>Journal of Mathematical Physics</i>. 1997;38(3):1289-1317. doi:<a href="https://doi.org/10.1063/1.531909">10.1063/1.531909</a> Erdös, L. (1997). Dia- and paramagnetism for nonhomogeneous magnetic fields. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href="https://doi.org/10.1063/1.531909">https://doi.org/10.1063/1.531909</a> Erdös, László. “Dia- and Paramagnetism for Nonhomogeneous Magnetic Fields.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 1997. <a href="https://doi.org/10.1063/1.531909">https://doi.org/10.1063/1.531909</a>. L. Erdös, Journal of Mathematical Physics 38 (1997) 1289–1317. Erdös L. 1997. Dia- and paramagnetism for nonhomogeneous magnetic fields. Journal of Mathematical Physics. 38(3), 1289–1317. 27272018-12-11T11:59:17Z2022-08-22T09:48:50Z