4 temperature both χ and ξ decrease rapidly with J$_{2}$ . for J$_{2}$ = 0 . 3, at T ≈ 1 . 25 (RGM data). The faster decay of the spin-spin correlators due to frustration is related to the decrease in the correlation length ξ with increasing J$_{2}$ , see the discussion below. FIG. 4: Correlation length ξ for J 2 = 0 , 0 . 1 , 0 . 2 , 0 . 3 , 0 . 4, from right to left. The inset shows the correlation length for T = 0 . 3 in dependence on the frustration J 2 . The solid line represents an exponential fit, ξ ( T = 0 . 3) ≈ 13 . 9 exp( − 6 . 4 J 2 ), of the data points (filled squares). FIG. 5: Uniform static spin susceptibility χ for (a) J 2 = 0 . 1 and (b) J 2 = 0 . 3 for N = 16 , 20 , 64 , 400 , thermodynamic limit (lines, RGM) and N = 16 , 20 (filled symbols, ED), from left to right. Note that for J 2 = 0 . 3 the curves for N = 400 and N → ∞ almost coincide. Since the susceptibility (together with the correlation length) is an important quantity to analyze the critical properties for T → 0, we first test the quality of our RGM approach in more detail by comparing the RGM data for N = 16 and N = 20 with ED data for the same system sizes, see Fig. 5. It is obvious, that the RGM and the ED data for χ are in excellent agreement. This is consistent with our previous finding 28 that for the 1D Heisenberg ferromagnet the RGM data for χ ( T → 0) and ξ ( T → 0) are in perfect agreement with exact Bethe ansatz results. Moreover, the RGM calculations of χ for finite N allow to estimate the magnitude of the finite-size effects. As can be clearly seen in Fig. 5, the finite-size effects at T ≲ 0 . 6 ( T ≲ 0 . 4) for J$_{2}$ = 0 . 1 ( J$_{2}$ = 0 . 3) be- come very large. Since the correlation length ξ becomes smaller with increasing J$_{2}$ (see the inset in Fig. 4), the finite-size effects become less pronounced with growing frustration. Nevertheless, based on our data we argue that the finite systems of N = 16 and N = 20, accessible The uniform static spin susceptibility χ and the cor- relation length ξ depicted in Figs. 3 and 4 show a sim- ilar behavior. Due to the ferromagnetic ground state, both quantities diverge at T = 0 exponentially, see be- low. With increasing frustration J$_{2}$ the rapid increase in both quantities is shifted to lower temperatures. As shown in the insets of Figs. 3 and 4, at a certain fixed FIG. 3: Uniform static spin susceptibility χ for J 2 = 0 , 0 . 1 , 0 . 2 , 0 . 3 , 0 . 4, from right to left. The inset shows the susceptibility for T = 0 . 3 in dependence on the frustration J 2 . The solid line represents an exponential fit, χ ( T = 0 . 3) ≈ 132 . 8 exp( − 9 . 7 J 2 ), of the data points (filled squares).  0  10  20  30  40  50  0  0.2  0.4  0.6  0.8  1  1.2  1.4 T 0 40 80 120  0 0.1 0.2  0.3 0.4 0.5 J$_{2}$ T=0.3  0  10  20  30  40  50 0  0.2  0.4  0.6  0.8  1 T (a)  0  10  20  30  40  50  0  0.2  0.4  0.6  0.8  1 (b)  0  2  4  6  8  10  0  0.2  0.4  0.6  0.8  1 T  0  4  8  12  0 0.1 0.2 0.3 0.4 0.5 J$_{2}$ T=0.3