Application of the ising model to the study of cluster multiplicities in finite excited systems

Abstract

Fragmentation is expected to be an experimental signal which can give some information about the physical characteristics of finite excited systems. We try to investigate the question concerning the mechanism which governs the onset of the disassembly of such systems in connection with their internal dynamics. We restrict this study to the case where the systems are in thermodynamical equilibrium. We use the 2-dimensional Ising model as a generic model in order to calculate the multiplicities for the formation of strongly bound clusters inside the system and analyse their behaviour as a function of the temperature. The calculated observables show features which reflect the role played by the internal dynamics. The evolution of the shape of the cluster multiplicities with temperature obtained in the present study is qualitatively the same as the one which comes out through different nuclear phase space fragmentation models. PACS

Microscopic model approaches to fragmentation of nuclei and phase transitions in nuclear matter

“…The degeneracy g is a complicated function of the link structure L. There exists some knowledge about it [165,166,169]. In fact g(a, s) differs from zero only in a narrow range of surfaces.…”

“…They describe Hamiltonian systems, hence they introduce an explicit, physical description of an N-body system. This was the main motivation for the introduction of the Ising model in order to interpret the cluster size distributions of an excited, fragmented system [169,203].…”

Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

“…In the recent past the success of percolation models [1] and their link with other generic approaches like Ising and Potts [2,3] has led to the development of many lattice models [4][5][6][7][8][9][10][11][12] which were used as sensible albeit schematic descriptions of excited disassembling nuclei. As simple as they may appear, their thermodynamic properties were considered as being at least qualitatively those of bound nucleon systems which interact essentially by means of the short range nuclear interaction.…”

Thermodynamics of a finite system of classical particles with short- and long-range interactions and nuclear fragmentation

“…We consider a 3-dimensional system of classical particles confined in a volume V = (Nd) 3 where N 3 is the number of cubic cells of linear dimension d (the extension to a parallelepipedic volume V = N 1 N 2 N 3 d 3 is straightforward). Each cell k is occupied by a particle (s k = 1) or empty (s k = 0).…”