5 ξ = √ ( α$_{0}$T − 1 + α$_{1}$ + α$_{2}$T ) exp ( β T ) . Note that the lead- ing power T − 1 in the preexponential functions was de- rived for the unfrustated case with the RGM in Ref. 37. We consider b , a$_{0}$ , a$_{1}$ , and a$_{2}$ as well as β , α$_{0}$ , α$_{1}$ , and α$_{2}$ as independent fit parameters. Recall that we can calcu- late RGM data only for temperatures down to a certain T$_{0}$ , where T$_{0}$ (e.g., T$_{0}$ = 0 . 161 for J$_{2}$ = 0 and T$_{0}$ = 0 . 052 for J$_{2}$ = 0 . 4) is the lowest temperature where the sys- tem of RGM equations converges (see Sec. II). Thus, in addition to the leading power T − 1 in the preexpo- nential function it is reasonable to consider higher order terms to achieve an optimal fit of the RGM data. For the fit we use 500 equidistant data points in the interval T$_{0}$ . . . T$_{0}$ + T$_{cut}$ , where T$_{cut}$ is set to 0 . 05. The fit of the numerical RGM data reproduces the analytical results of Ref. 37 for J$_{2}$ = 0, i.e., b ( J$_{2}$ = 0) = 2 β ( J$_{2}$ = 0) = π/ 2, with a precision of four digits. After having tested our fitting procedure by compar- ison with the analytical predictions for J$_{2}$ = 0, we now consider the frustrated model, where (to the best of our knowledge) no other results are available. From our nu- merical data for χ and ξ we determine the J$_{2}$ dependence of the coefficients b and β . We find that the numerical data for b and β obtained by the fitting procedure de- scribed above are very well described by a linear decrease in both parameters with increasing frustration, b = 2 β = − π 2 ( J$_{1}$ + 2 J$_{2}$ ) . (11) Obviously, both parameters would be zero at the classi- cal transition point J$_{2}$ = 0 . 5, but they are still finite at the transition point J c 2 ≈ 0 . 44 of the quantum model. Hence, the exponential divergence is present in the full parameter range J$_{2}$ ≤ J c 2 where the ground state is fer- romagnetic. We emphasize that this result is contrary to the behavior observed for the 1D frustrated spin-1 / 2 ferromagnet, where the critical properties change at the zero-temperature transition point. 28 We mention further that the leading coefficients a$_{0}$ and α$_{0}$ of the preexponen- tial functions, see the expressions for χ and ξ given above, vanish at the transition point J c $_{2}$, whereas the next coeffi- cients a$_{1}$ and α$_{1}$ remain finite at J c $_{2}$. Hence, the preexpo- nential temperature dependence is changed approaching the zero-temperature transition. Another interesting quantity is the specific heat C$_{V}$ shown in Fig. 6. For J$_{2}$ = 0 the specific heat ex- hibits a typical broad maximum at about T = 0 . 562. Increasing the frustration the height of this maximum becomes smaller and it is shifted to lower temperatures. Let us mention, that the linear decrease in the coef- ficients b and β , see Eq. (11), found by fitting the low- temperature behavior of χ and ξ is the same as that ob- tained analytically for the zero-temperature spin-stiffness ρ$_{s}$ , see Sec. II. This relation between ρ$_{s}$ and the diver- gence of the correlation length and the susceptibility is in accordance with general arguments 48,49 concerning the low-temperature physics of low-dimensional Heisenberg ferromagnets. Next we use the RGM results to determine the co- efficients b and β as functions of J$_{2}$ . We assume that the general low- T behavior of these quantities is pre- served for 0 < J$_{2}$ < J c $_{2}$, cf. Ref. 28, and fit our nu- merical RGM data for χ and ξ at low temperatures us- ing the ansatzes χ = ( a$_{0}$T − 1 + a$_{1}$ + a$_{2}$T ) exp ( b T ) and Next we use the RGM for N → ∞ to investigate the critical behavior of χ and ξ for T → 0 in more detail. We start with a brief discussion of the low- temperature behavior of the unfrustrated ferromagnet. Contrary to the 1D case, where for J$_{2}$ = 0 exact Bethe results are available, 47 we have only approximate re- sults for the 2D model. From low-temperature expan- sions of the susceptibility and the correlation length for the model with J$_{2}$ = 0 using renormalization group approaches, 30,31 the modified spin-wave threory, 29 and the RGM 37 it is known that for T → 0 the susceptibility behaves as χ ∝ T $^{s}$exp ( b/T ) and the correlation length as ξ ∝ T σ exp ( β/T ). While different leading exponents s and σ for the (less important) preexponential factor were obtained by different methods, the exponential di- vergence is obtained by all authors. 29–31,37 However, dif- ferent values for the coefficients b and β were reported, namely, b ( J$_{2}$ = 0) = π/ 2 using RGM, 37 b ( J$_{2}$ = 0) = π us- ing modified spin-wave theory 29 or renormalization group approach, 30 and b ( J$_{2}$ = 0) = 0 . 1327 π using a different version of the renormalization-group approach. 31 In all these papers 29–31,37 it was found that the coefficients in the exponents fulfill the relation β = b/ 2. We mention further, that early numerical studies based on quantum Monte-Carlo calculations (using, however, χ and ξ data only for quite large temperatures) give b ( J$_{2}$ = 0) ≈ 4 . 5 ≈ 1 . 43 π (Ref. 33) and β ( J$_{2}$ = 0) = 0 . 254 π (Ref. 32). Let us finally argue, that the results for the coefficient b ob- tained by modified spin-wave theory 29 as well as renor- malization group approach 30 and by the RGM 37 seem to be most reliable, since these methods are well-tested. Moreover, for the 1D spin-1 / 2 Heisenberg ferromagnet it was shown that the RGM 28,37 as well as the modified spin-wave theory 29 reproduce the exact Bethe-ansatz re- sults for the low-temperature behavior of χ and ξ . Hence, it is to some extent surprising, that there is a difference by a factor of 2 in the coefficient b between the value ob- tained by modified spin-wave theory 29 (as well as renor- malization group approach $^{30}$) and the RGM for the 2D unfrustrated ferromagnet. This discrepancy is a known but unresolved problem. 35,37 However, we believe that our general conclusions concerning the exponential diver- gence of the frustrated model, see the discussion below, are not affected by this problem. by exact full diagonalization, are not representative for the thermodynamic limit, see also Refs. 16 and 17. Note that for the 1D case, the ED data for N = 20 are in good agreement with RGM data for N → ∞ . 28 Consis- tent to that observation, in two dimensions the system of N = 400 sites with the same linear extension is already close to the thermodynamic limit, see Fig. 5.