-1 -0.8 -0.6 -0.4 -0.2  0  0.2  0.4 -3 -2 -1  0  1  2  3 /2 ... WF-FP in LPA WF-FP in LPA WF-FP at NLO WF-FP at NLO lines of fixed points ( /2)  0  0.01  0.02  0.03  0.04  0.05  0.06  0  2  4  6  8  10  12 ( a 2 ) broken SuSy unbroken SuSy 2 4 6 7 FIG. 3. Left panel: Lines of fixed points in the η - γ plane (solid curves) and the anomalous dimension as a function of γ = 2 λ as obtained from Eq. (34) (dotted curve). Right panel: Phase diagram in the plane spanned by the dimensionless couplings specified at the cutoff scale Λ as obtained from truncations with n = 1 ( φ $^{2}$), n = 2 ( φ $^{4}$), and n = 3 ( φ $^{6}$) in Eq. (24). the mass is given by whereas for unbroken supersymmetry it is given by In the broken phase a polynomial expansion of the su- perpotential is justified 7 and we find From the scaling of the couplings for k → 0, we read off that the mass scales as This scaling behavior is demonstrated in Fig. 4 for a trun- cation with n = 4, i. e. an expansion of w ′ up to order ϕ 8 ∼ φ $^{8}$, see also Eq. (24). Due to our analysis of the convergence of the fixed-point values of the couplings λ and b$_{2}$$_{i}$ as well as the anomalous dimension η$_{∗}$ , see Tab- ular I, II and III, we expect that the truncation order n = 4 is already sufficient to capture qualitatively and quantitatively most of the features of the zero- and finite- temperature phase diagram, see also Sect. IV B. From a linear fit to the double-logarithmic plot of m ( k ) we find m ( k ) ∼ k 0 . 23 which is indeed reasonably close to the expected scaling given in Eq. (41). The reason for this behavior, which is very different from the one found in where the field φ$_{0}$ minimizes V . In the case of broken supersymmetry (and unbroken GLYPH<CI> $_{2}$) we have φ$_{0}$ = 0 and The breaking of supersymmetry is driven by the un- stable direction a $^{2}$, similarly as in two dimensions [13]. In the plane spanned by the values of the dimensionless couplings λ and λa 2 given at the cutoff-scale Λ we find a transition line for supersymmetry breaking, see Fig. 3 (right panel). From the effective potential V = lim$_{k}$$_{→}$$_{0}$ W ′ 2 k / 2, we read off the mass of the boson, 7 Note that for unbroken supersymmetry a polynomial expansion is bound to fail and one needs to solve the partial differential equation in order to determine the boson mass. m 2 bos = W ′ k → $_{0}$( φ$_{0}$ ) W ′′′ k → $_{0}$( φ$_{0}$ ) + W ′′ 2 k → $_{0}$( φ$_{0}$ ) , (36) m ( k ) ∼ k 1 4 for k ≪ Λ . (41) λ$_{∗}$ ∼ const. and a 2 ∼ k − 3 2 , (40) m 2 $_{broken}$( k ) = W ′ $_{k}$(0) W ′′′ k (0) = 2 k $^{2}$λ$^{2}$a$^{2}$. (39) C. Zero-temperature phase diagram and scaling of the mass FIG. 4. Logarithm of the boson mass as a function of the RG- scale k . A linear fit to the data points yields m ( k ) ∼ k 0 . 23 for k ≪ Λ. m 2 broken = W ′ k → $_{0}$(0) W ′′′ k → $_{0}$(0) , W ′′ k → $_{0}$(0) = 0 , (37) m 2 unbroken = W ′′ 2 k → $_{0}$( φ$_{0}$ ) , W ′ k → $_{0}$( φ$_{0}$ ) = 0 . (38) -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -9 -8.5 -8 -7.5 -7 -6.5 -6 -5.5 -5 -4.5 -4 ln(m(k)) ln(k)$^{results}$ from the flow equation f(x)=0.23*x-0.82