Temperature crossovers in cuprates

We study the temperature crossovers in cuprates using a nearly antiferromagnetic Fermi liquid model. For overdoped cuprates, we find a crossover between a Fermi-liquid behavior at low $T<T_{cr}$ and a mean-field, $z=2$ behavior at high temperatures ($z$ is the dynamic critical exponent). We argue that the in-plane resistivity is linear in $T$ above $T_{cr}$ due to the proximity of the quasiparticle Fermi surface to the magnetic Brillouin zone boundary. For underdoped cuprates, we argue that in order to account for the experimentally measured sequence of crossovers from a mean-field, $z=2$ behavior at high temperatures to $z=1$ scaling behavior at intermediate $T$, and pseudogap behavior at even lower $T$, one has to take into consideration the thermal variation of the damping rate of spin fluctuations, $\gamma$. We further argue that the primary source for the variation of $\gamma$ with $T$ in the underdoped cuprates is the thermal evolution of the quasiparticle spectral weight.