We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies - an effective spin-fermion interaction ḡ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ ḡ/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem - the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours - which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(logλ) terms in the RG formalism. We apply this technique to study the properties of the spin-fermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for the cuprates, and argue that the spin-fermion model is capable of explaining the anomalous normal state properties of the high Tc materials. We also show that the conventional φ4 theory of the quantum-critical behaviour is inapplicable in 2D due to the singularity of the φ4 vertex.
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It is our pleasure to thank A. M. Finkel’stein for stimulating discussions on numerous aspects of strong coupling effects in the cuprates. We are also thankful to E. Abrahams, A. A. Abrikosov, B. L. Altshuler, D. Basov, G. Blumberg, J. C. Campuzano, S. Caprara, C. Castellani, C. Di Castro, P. Coleman, L. P. Gor’kov, M. Grilli, L. Ioffe, P. Johnson, R. Joynt, B. Keimer, R. Laughlin, M. Lavagna, D. Khveschenko, G. Kotliar, H. von Löhneysen, A. Millis, M. Norman, C. Pépin, D. Pines, A. Rosh, S. Sachdev, Q. Si, O. Tchernyshov, A. Tsvelik, J. Tu and J. Zasadzinski for useful conversations. We are also thankful to D. Basov and J. Tu for sharing their unpublished results with us and to M. Norman for bringing refeference  to our attention. The research was supported by NSF DMR-
9979749 (Ar.A and A.Ch.), and by the Ames Laboratory, operated for the US Department of Energy by Iowa State University under contract No. W-7405-Eng-82 (J.S.). This work was partly done while A.C. was on a sabbatical leave at the Rutgers University and the NEC Research Institute. The hospitality of both places is acknowledged with thanks.