6 Interestingly, within our RGM approach the shape of the J c $_{2}$, where the ferromagnetic ground state breaks down, is J c 2 ≈ 0 . 44 | J$_{1}$ | . We tested the method by comparing RGM data for the spin-spin correlation functions and the uniform sus- ceptibility χ calculated for finite lattices of N = 16 and N = 20 sites with corresponding exact-diagonalization data for the same lattice sizes and found a good agree- ment between both methods. However, the comparison of RGM data for finite lattices and for N → ∞ indicates strong finite-size effects at low temperatures. This leads to the conclusion that the finite systems of N = 16 and N = 20 are not representative for the low-temperature thermodynamics of large systems. As it is known from the Mermin-Wagner theorem 50 the thermal fluctuations are strong enough to suppress magnetic LRO for the Heisenberg ferromagnet in dimen- sion D < 3 at any finite temperature. Due to frustration the fluctuations are further enhanced. Thus, frustration leads to a significant suppression of magnetic correlations at finite temperatures even if the ground state remains ferromagnetic. The low-temperature behavior of the susceptibility χ and the correlation length ξ in the ferromagnetic ground- state region J$_{2}$ < J c 2 exhibits the exponential divergences χ ∝ exp ( π ( | J$_{1}$ |− 2 J$_{2}$ ) 2 T ) and ξ ∝ exp ( π ( | J$_{1}$ |− 2 J$_{2}$ ) 4 T ) . Al- though the numerator in the exponent decreases with growing J$_{2}$ the exponential divergence perpetuates in the whole parameter region J$_{2}$ ≤ J c $_{2}$. The specific heat calculated within the RGM exhibits a double-maximum structure for J$_{2}$ ≳ 0 . 34 analogous to the 1D model. To test our theoretical predictions it would be inter- esting to reconsider experimentally quasi-2D spin-1/2 ferromagnets, such as K$_{2}$CuF$_{4}$, Cs$_{2}$CuF$_{4}$, Cs$_{2}$AgF$_{4}$, La$_{2}$BaCuO$_{5}$, and Rb$_{2}$CrCl$_{4}$ 23–27 with respect to a possible frustration and its influence on low-temperature thermodynamics. C$_{V}$ ( T ) curve changes for large frustration. For J$_{2}$ ≳ 0 . 34 the specific heat shows two maxima, one at low tempera- tures ( T < 0 . 193) and another one at high temperatures ( T > 0 . 6). This extra low-temperature maximum signals the emergence of an additional low-energy scale when ap- proaching the transition point J c $_{2}$. Then many low-lying multiplets appear above the fully polarized ferromagnetic ground-state multiplet. Hence, the appearance of the additional low-temperature maximum in C$_{V}$ ( T ) can be attributed to a subtle interplay between all of these low- lying states. Note that a similar behavior was found for the 1D case. 28 IV. SUMMARY Acknowledgments: This work was supported by the DFG (project RI615/16-1 and DR269/3-1). For the exact diagonalization J. Schulenburg’s spinpack was used. J.R. thanks N.B. Ivanov for useful discussions. In this paper we investigated the influence of the frus- trating NNN coupling J$_{2}$ < J c 2 on the thermodynamic properties of the 2D spin-1/2 Heisenberg ferromagnet us- ing the spin-rotation-invariant Green’s function method (RGM). The RGM estimate for the critical frustration FIG. 6: Specific heat calculated by RGM for J 2 = 0 , 0 . 1 , 0 . 2 , 0 . 3 , 0 . 35, and 0 . 4, from top to bottom. The inset shows the specific heat for J 2 = 0 . 3 to 0 . 35 in steps of 0 . 01.  0  0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  0  0.5  1  1.5  2 C V T 0.1 0.15  0 0.4  0.8 T C V 1 Frustrated Spin Systems , H. T. Diep, Ed. (World Scientific, Singapore, 2004). 2 Quantum Magnetism , U. Schollw¨ ock, J. Richter, D. J. J. Farnell, R. F. Bishop, Eds. (Lecture Notes in Physics, 645 ) (Springer, Berlin, 2004). 3 P. Chandra and B. Doucot, Phys. Rev. B 38 , 9335 (1988); H.J. Schulz and T.A.L. Ziman, Europhys. Lett. 18 , 355 (1992); H.J. Schulz, T.A.L. Ziman, and D. Poilblanc J. Phys. I 6 , 675 (1996); J. Richter, N.B. Ivanov, and K. Retzlaff, Europhys. Lett. 25 , 545 (1994); A. E. Trumper, L. O. Manuel, C. J. Gazza, and H. A. Ceccatto, Phys. Rev. Lett. 78 , 2216 (1997); L. Capri- otti, F. Becca, A. Parola, and S. Sorella, Phys. Rev. Lett. 87 , 097201 (2001); R.R.P. Singh, Weihong Zheng , J. Oit- maa, O.P. Sushkov, and C.J. Hamer, Phys. Rev. Lett. 91 , 017201 (2003); J. Sirker, Z. Weihong, O. P. Sushkov, and J. Oitmaa, Phys. Rev. B 73 , 184420 (2006); R. Dar- radi, O. Derzhko, R. Zinke, J. Schulenburg, S. E. Kr¨ uger, and J. Richter, Phys. Rev. B 78 , 214415 (2008); V. Murg, F. Verstraete, and J. I. Cirac, Phys. Rev. B 79 , 195119 (2009), J. Richter and J. Schulenburg, Eur. Phys. J. B 73 , 117 (2010).