The recent results obtained within the exactly solvable models [11, 12] also justify the parameterization (6) and show that the only physical reason of degeneration of the first order deconfinement phase transition at low bary- onic densities into a cross-over is negative surface tension coefficient in this region. Moreover, an existence of nega- tive surface tension at the cross-over region was directly demonstrated from the lattice QCD data very recently within a new phenomenological model of the confinement [18]. An actual choice of the continuous functions σ ± of tem- perature T and baryonic chemical potential µ along with parameterization of the nil line of the surface tension co- efficient T$_{Σ}$ ( µ ) for the tricritical and critical endpoint of the QCD phase diagram can be found in [11] and [12], respectively. The spectrum (3) has a simple form, but is rather gen- eral since both the width Γ( v ) and the bag mass density B can be medium dependent. It clearly reflects the fact that the QGP bags are similar to the ordinary quasipar- ticles with the medium dependent characteristics (life- time, most probable values of mass and volume). In principle, one could consider various v -dependences Γ( v ), but in [8, 9] it was shown that the only square root dependence of the resonance width on its volume, i.e. Γ( v ) = γv 1 2 , does not lead to the problems with the large QGP bags existence. For large bag volumes ( v ≫ M$_{0}$/B > 0) the factor (5) can be found as N$_{Γ}$ ≈ 1 $_{/}$√$_{2}$$_{π}$$_{. Similarly, one can show}$ that for heavy free bags ( m ≫ BV$_{0}$ , V$_{0}$ ≈ 1 fm 3 [8], ignoring the hard core repulsion and thermostat) It originates in the fact that for heavy bags the Gaussian in (3) acts like a Dirac δ -function for Γ( v ) = γv 1 2 . Sim- ilarly to (7), one can estimate the width of heavy free bags averaged over bag volumes and get Thus, the mass spectrum of heavy free QGP bags is the Hagedorn-like one with the property that heavy res- onances must have the large mean width and, hence, they are hardly observable. This resolves the conceptual problem of the deficit of observed heavy hadronic reso- nances compared to the Hagedorn mass spectrum. Ap- plying these arguments to the strangelets, we conclude that, if their mean volume is a few cubic fermis or larger, they should survive a very short time, which is similar to the results of Ref. [19] predicting an instability of such strangelets. An analysis of the full spectrum (1) allows one to de- termine the pressure of the QGP bags [8] which shows two drastically different regimes depending the value of the most probable mass of a bag ( v ≫ V$_{0}$ ) For T ≤ T$_{Σ}$ ( µ ) such a parameterization is justified by the usual cluster models like the FDM [13] and SMM [14–17], whereas the general consideration for any T can be driven by the surface partitions of the Hills and Dales model [10]. Also the volume spectrum in (4) contains the surface free energy ( κ = 2 / 3) with the T -dependent surface ten- sion which can be parameterized in a general way [10–12] The normalization factor obeys the condition In (1) s denotes the variable of the isobar ensemble which is dual to the system volume. An exponential exp( − sv ) in (1) describes the hard core repulsion between the bags [8], while the density of states ρ ( m, v ) of bags of mass m and volume v has the form The main object of the FWM is the mass-volume spec- trum of heavy and large QGP bags at temperature T ( V$_{0}$ ≈ 1 fm $^{3}$, M$_{0}$ ≈ 2 . 5 GeV [8, 9]) 2 are given in Sec. 4. II. FWM OF QGP BAGS F$_{Q}$ ( s, T ) = ∞ ∫ V$_{0}$ dv ∞ ∫ M$_{0}$ dm ρ ( m, v ) exp( − sv ) φ ( T, m ) , (1) φ ( T, m ) = ∞ ∫ 0 p $^{2}$dp exp [ − ( p 2 + m $^{2}$)1 / 2 T ] . (2) where the thermal density of bags of mass m reads as The constants a > 0 and b > 0 are discussed in [8]. $_{N}$− 1 Γ = ∞ ∫ M$_{0}$ dm Γ( v ) exp [ − ( m − Bv ) 2 2Γ $^{2}$( v ) ] . (5) σ ( T, µ ) =    σ − > 0 , T → T$_{Σ}$ ( µ ) − 0 , 0 , T = T$_{Σ}$ ( µ ) , σ + < 0 , T → T$_{Σ}$ ( µ ) + 0 . (6) Γ( v ) ≈ Γ( m/B ) = γ √ m B . (8) ρ ( m ) ≡ ∞ ∫ V$_{0}$ dv ρ ( m, v ) ≈ ρ$_{1}$ ( m $_{B}$) B m a + 3 2 exp [ m T$_{H}$ ] . (7) 〈 m 〉 ≡ Bv + Γ $^{2}$( v ) β , with β ≡ $_{T}$− 1 H − T − $^{1}$. (9) ρ ( m, v ) = ρ$_{1}$ ( v ) N$_{Γ}$ Γ( v ) m a + 3 2 exp [ m T$_{H}$ − ( m − Bv ) 2 2Γ $^{2}$( v ) ] , (3) ρ$_{1}$ ( v ) = f ( T ) v − b exp [ − σ ( T ) T v κ ] . (4) As one can see from (3) the the density of states has a Hagedorn like parameterization with respect to mass and the Gaussian attenuation around the bag mass Bv ( B is the mass density of a bag of a vanishing width) with the volume dependent Gaussian width Γ( v ) or width hereafter. We will distinguish it from the true width defined as Γ$_{R}$ = α Γ( v ) ( α ≡ $_{2}$√$_{2 ln 2 ).}$ As shown in [8, 9] the Breit-Wigner attenuation of a resonance mass cannot be used in the spectrum (3) because in this case the finite width leads to a divergency of the mass integral in (1) above T$_{H}$ .