ω ∼ k$_{y}$ . As this region is separated from the mass shell, instead of the self-energy it is more convenient to study the Green function itself. It is also convenient to discuss the amputated propagator, ¯ Σ$_{ω}$( k ) = G$_{ω}$ ( k ) [ G (0) ω ( k ) ] − $^{2}$. To the second order in J , ¯ Σ$_{ω}$( k ) is given by Eq. (12), and is singular at ω = k$_{y}$ . At the next, fourth order, the correction (see App. B) has stronger singularity In what follows we resum the most singular terms in the expansion of ¯ Σ to all orders in J . For n ≥ 2 we introduce new variables, and integrating over y$_{i}$ s variables we write the correction of order (2 n ) to the amputated Green function as where the remaining integrals are convergent at the upper limit, and can be evaluated as As a result we obtain for the singular part For n = 1 the last expression reduces to the second order corrections, Eq. (12). The sum of singular contributions Eq. (33) yields the result of Eq. (9). First we would like to make a remark about the easy axis anisotropy regime where the phase transition is in the Ising model universality class. From our calculations it is easy to see that as far as the singular terms are concerned, the results remain unchanged provided one considers only one particular value for the scaling dimen- sion: d = 1 / 8. This is despite the fact that multipoint correlation functions of the Ising model order parame- ter fields are more complicated than (19). However, the In the present appendix we evaluate the most singular corrections to the self-energy at the mass shell, ω ∼ k$_{x}$ . We are grateful to A. Chubukov for encouraging dis- cussions and interest to the work. We acknowledge sup- port by the US DOE under contract number DE-AC02- 98 CH 10886. This research was also supported as part of the Center for Emerging Superconductivity funded by the U.S. Department of Energy, Office of Science. M. Khodas acknowledges support from BNL LDRD grant 08-002. Although our model does not include all the features ascribed to the cuprates, the results obtained may serve as a good qualitative guide to the problem. For instance, we see that critical thermal fluctuations give rise to the characteristic linear temperature dependence ∼ T of the spectral peak width. This is an indication that such fluc- tuations are responsible of this feature in the cuprates. Our results demonstrate that with the rise of temperature the renormalized mass shell identified as the maximum intensity line in Fig. 4 approaches the bare Fermi surface, while the peak becomes rather incoherent. The back- side of the Fermi pockets fades away so that the pockets now look like arcs. These effects are qualitatively simi- lar to that of the quantum fluctuations studied in Ref. [6] though the intensity of quantum fluctuations is regulated not by temperature, but by the interactions. In summary, we have presented systematic study of the thermal fluctuations effects in two-dimensional sys- tem of electrons in interaction with SDW order param- eter. In particular the spectral density has been found to be strongly sensitive to these fluctuations. Fluctua- tions tend to restore the non-interacting Fermi surface topology thus overriding the effects of the SDW order. Now we can discuss the results. They are well illus- trated by Figs. 1,4. The region of applicability of our calculations involves the energy scale T$_{K}$ = J ( Ja ) d/ ( d − $^{1)}$. The result at the mass shell is valid for | k$_{y}$ | > T$_{K}$ and the result at the shadow mass shell holds at | k$_{x}$ | > T$_{K}$ . With increasing temperature the spectral weight is transferred towards the bare Fermi surface and the shadow band fea- ture quickly fades away as is clearly seen on figure (4) where the darker areas correspond to large values of the spectral density. singularities are determined by more simple correlators, namely by the diagrams where pairs of the operators are very close to each other (see Fig. 3) resulting in a fusion of two order parameter fields. In the Ising model such fusion generates the energy density operator and in the XY-model it generates the gradient of φ field. Both op- erators have the same multi-point correlation functions. 5 ¯ Σ (4) ≈ i( Ja $^{d}$) $^{4}$Γ(1 − 2 d )Γ(2 − 2 d ) ( − i( ω − k$_{x}$ )) 3 − 4 d α 2 − 2 d . (28) Y ξ$_{1}$ = x$_{1}$ − 0 , Y ξ$_{2}$ = x$_{2}$ − x$_{1}$ , . . . . . . , Y ξ$_{n}$$_{−}$$_{1}$ = X − x$_{n}$$_{−}$$_{2}$ , (29) ¯ Σ (2 n ) = ( − i) 2 n − $^{1}$( Ja $^{d}$) 2 n ( − i( ω − k$_{x}$ )) 2 n (1 − d ) − 1 × Γ[2 n (1 − d ) − 1] ( n − 1)! ¯ I$_{n}$ ( α ) , (30) ¯ I$_{n}$ ( α )=$^{n}$$^{−}$$^{1}$ ∏ i =1 ∫ ∞ 0 dξ$_{i}$ ξ − 2 d 1 · · · ξ − 2 d n − 1 ( α − $^{1}$+ ξ$_{1}$ + . . . + ξ$_{n}$$_{−}$$_{1}$ ) 2 n (1 − d ) − 1 (31) ¯ I$_{n}$ ( α ) = α n − 2 $_{d}$Γ n − $^{1}$(1 − 2 d )Γ( n − 2 d ) Γ(2 n (1 − d ) − 1) . (32) ¯ Σ (2 n ) = i( − i Ja $^{d}$) 2 $^{n}$αn − 2 $^{d}$Γn − $^{1}$(1 − 2 d )Γ( n − 2 d ) ( n − 1)!( − i( ω − k$_{x}$ )) 2 n (1 − d ) − 1 . (33) Acknowledgments V. CONCLUSIONS Appendix A: Perturbation theory at the mass shell.