Fig. 4: Analysis using cv and SKelvin.
From: Quantitative assessment of the universal thermopower in the Hubbard model
Color density plots of −∂2s/(∂p∂T) calculated from doping derivative of specific heat [\(-{(\partial {c}_{v}/\partial p)}_{T}/T\), (a, c)] and temperature derivative of SKelvin [\(-e{(\partial {S}_{{{{{{{{\rm{Kelvin}}}}}}}}}/\partial T)}_{p}\), (b, d)], for interaction strengths U/t = 6 (a, b) and U/t = 8 (c, d), both with \({t}^{{\prime} }/t=-0.25\). A cubic-spline fit was applied to curves of cv versus p and SKelvin versus T, with corresponding derivatives obtained from the fits. The derivatives −∂2s/(∂p∂T) were interpolated (cubic) onto the two-dimensional (p, T) plane. Horizontal dashed lines mark the leading-order approximation for the spin-exchange energy J = 4t2/U, and solid lines mark the contour where −∂2s/(∂p∂T) = 0.
