The statistical multifragmentation model for liquid–gas phase transition with a compressible nuclear liquid

Abstract

We propose a new formulation of the statistical multifragmentation model based on the analysis of the virial expansion for a system of the nuclear fragments of all sizes. The developed model not only enables us to account for short-range repulsion, but also to calculate the surface free energy which is induced by the interaction between the fragments. We propose a new parameterization for the liquid phase pressure which allows us to introduce a compressible nuclear liquid into the statistical multifragmentation model. The resulting model is exactly solvable and has no irregular behavior of the isotherms in the mixed phase region that is typical for mean-field models. The general conditions for the 1-st and 2-nd (or higher) order phase transitions are formulated. It is shown that all endpoints of the present model phase diagram are the tricritical points, if the Fisher exponent τ is in the range 3 2 ≤ τ ≤ 2. The treatment of nuclear liquid compressibility allows us to reduce the tricritical endpoint density of the statistical multifragmentation model to one third of the normal nuclear density. A specific attention is paid to of the fragment size distributions in the region of a negative surface tension at supercritical temperatures.

Geometrical clusterization and deconfinement phase transition in SU(2) gluodynamics

“…3). This remarkable result is in line with framework of the statistical cluster models [7,8,11]. Thus, a four parametric fit (n par = 4) of the LDF yields k min = 2 and τ = 1.806 ± 0.008 both for clusters and for anticlusters.…”

“…A determination of the Fisher topological constant τ = 1.806±0.008 with high precision is another important result of this study. The found value of τ is the same both for clusters and for anticlusters and it agrees with the prediction of an exactly solvable model of the nuclear liquid-gas PT [11], while it contradicts to the FDM [8]. Our analysis of the reduced surface tension coefficient and the mean size of the largest (anti)cluster allowed us to conclude that these quantities can serve as an order parameters of the deconfinement PT in SU(2) gluodynamics.…”

“…2). The found distributions closely resemble the ones discussed for the nuclear fragments [11] and for the Ising spin clusters [12]. Hence, we analyzed whether the Liquid Droplet Formula (LDF) [7] n th…”

“…Thus, a four parametric fit (n par = 4) of the LDF yields k min = 2 and τ = 1.806 ± 0.008 both for clusters and for anticlusters. It is necessary to stress that the found value of τ agrees with the exactly solvable model of the nuclear liquid-gas PT [11] which has a tricritical endpoint, but it contradicts to the FDM [7,8] which has a critical endpoint. Fixing the values of τ and k min we could perform a three parametric fit (n par = 3) of the (anti)cluster size distributions to define C A , µ A and σ A with higher precision and less time for simulations.…”

Effects of Induced Surface Tension in Nuclear and Hadron Matter

“…Foremost, the problem is related to the wrong values of the third, the fourth and higher virial coefficients generated by the Van der Waals EoS. As it was shown in [1] the solution of this problem requires to account for the fact that at low densities an interparticle hard-core repulsion is well described by the excluded volume approximation, whereas the high density regime is controlled by the proper volume of particles. The Van der Waals prescription is not able to switch between these two regimes and, therefore, it requires for an improvement.…”