Comment on “Negative heat capacities and first order phase transitions in nuclei”

Abstract

In a recent paper L.G. Moretto et al [1] claim that the negative heat capacities presented in our previously published paper [2] are "artifacts" coming from the use of periodic boundary conditions in the Lattice-Gas calculations. We stress in this comment that this claim is wrong: in ref.[2] we did not use periodic boundary conditions and anyhow the boundary conditions are irrelevant for the statistical ensemble used in [2]. The second claim of [1] is that, because of the Coulomb repulsion, systems "with A > 60 should present no anomalous negative heat capacities". We show that this conclusion is contradicted by exact Lattice-gas simulations including Coulomb forces which present negative heat capacities even for A > 200.Let us start with the discussion about the boundary conditions. It is clearly stated in ref.[2] that"L 3 [the lattice size] is large enough (typically greater than 20 3 lattice sites) so that the boundary conditions do not affect the calculations with a constraining λ." This means that the results of ref.[2] do not depend upon the conditions used at the boundary, and in fact the calculations were made without periodic boundary conditions. At that time we checked the independence of the boundaries comparing N = 8000 and N = 27000 lattices. To see a sizeable effect of the boundary, we have decreased the size of the lattice. A fast calculation of 50000 events for 216 particles in a N = 5832 lattice at an energy E = 0.4ǫ confined by a Lagrange multiplier log λ = −8 , gives a temperature T = (0.687 ± 0.004)ǫ, a heat capacity C = −16.3 ± 0.2, and a kinetic energy fluctuation σ 2 k /T 2 = 1.64 ± 0.03. If periodic boundary conditions are imposed, the temperature becomes T = (0.682 ± 0.004)ǫ, the heat capacity C = −16.9 ± 0.4 and the fluctuation σ 2 k /T 2 = 1.63 ± 0.07. The temperature decrease in the phase transition region is ∆T = (7.6 ± 0.4)10 −3 ǫ (∆T = (6.7 ± 0.6)10 −3 ǫ) with (without) periodic boundary conditions. This shows that the boundary conditions do not affect the thermodynamics. Indeed, in ref.[2] we have analyzed an ensemble of particles in the vacuum for which only the average spatial extension of the system is defined (isobar ensemble). Then, provided that the lattice in which the system has still to be discretized for technical reasons is big enough, boundary conditions are irrelevant since the particles never explore the outer region.In a previous paper [3] we have considered a canonical Lattice Gas model in a box of constant volume (isochore ensemble), and there we have used periodic boundary conditions. In these calculations negative compressibilities are reported but the heat capacity is always positive. In fact, in the canonical ensemble the heat capacity is proportional to the energy variance and can never be negative [4].Concerning the isochore microcanonical ensemble, the published results [5] show that the heat capacity at constant volume C V is always positive. Therefore, contrary to what is claimed in ref.[1], published results dealing with Lattice Gas calculations with typ...

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