Zipf's Law in the Liquid Gas Phase Transition of Nuclei

Abstract

Zipf's law in the field of linguistics is tested in the nuclear disassembly within the framework of isospin dependent lattice gas model. It is found that the average cluster charge (or mass) of rank $n$ in the charge (or mass) list shows exactly inversely to its rank, i.e., there exists Zipf's law, at the phase transition temperature. This novel criterion shall be helpful to search the nuclear liquid gas phase transition experimentally and theoretically. In addition, the finite size scaling of the effective phase transition temperature at which the Zipf's law appears is studied for several systems with different mass and the critical exponents of $\nu$ and $\beta$ are tentatively extracted.