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Universal logarithmic temperature dependence of magnetic susceptibility of one-dimensional electrons at critical values of magnetic field

We study the leading low temperature dependence of magnetic susceptibility of one-dimensional electrons with fixed total number of particles at the magnetic fields equal to zero temperature critical values where magnetic field induces commensurate-incommensurate quantum phase transitions. For free and repulsively interacting electrons there is only one such critical field corresponding to the transition to the fully polarized state. For attractively interacting electrons besides saturation field there is another critical field equal to the spin gap where zero temperature magnetization sets in. For all cases, except of the lattice models at half filling, the magnetic susceptibility at critical values of magnetic field has a universal logarithmic temperature dependence,x(T)=x(0)(1+2/Log(T)+...) for T -> 0.