The three-dimensional Ising model and its Fisher analysis: A paradigm of liquid-vapor coexistence in nuclear multifragmentation

Recent analysis of multifragmentation data in terms of Fisher’s droplet model has led to the extraction of the nuclear liquid-vapor phase diagram. A similar analysis of Coniglio-Klein clusters of the $d=3$ Ising model shows an equivalently good Fisher’s scaling which can be used to obtain the Ising phase diagram, thus supporting the claim of the nuclear multifragmentation analysis in terms of a phase transition.

Figure 1

The probability distributions for obtaining $m$ clusters of size $A$ at the three temperatures indicated. The solid lines are Poisson distributions with means given by the Monte Carlo data.

Figure 2

(Color online) Arrhenius plots of the cluster distributions. A statistical error bar is shown when it exceeds the size of the data point. The lines are fits of the form given in Eq. (1). The critical temperature is indicated by the dashed line.

Figure 3

The upper panel shows the extracted “barriers” from the fits to the cluster distributions. The line is a fit of the form given in Eq. (3). The lower panel shows the power law behavior of the cluster distribution at $k_{B}T∕J=4.515$. The line is a fit of the form given in Eq. (6). In both panels, error bars are smaller than the data point.

Figure 4

(Color online) Scaling behavior of cluster distributions for the Ising model and for nuclear multifragmentation data. The nuclear multifragmentation yields have been scaled by a factor of $100$ to offset the data from the Ising cluster yields and scaled by another factor to account for the Coulomb energy present, see Refs. 9, 10 for details.

Figure 5

The magnetization as a function of reduced temperature. The open circles show the magentization predicted via Fisher’s droplet model (see text) and the solid line shows a parametrization for the magnetization.