From: Lopez, Jorge
Sent: Thursday, January 19, 2006 6:22 PM
To: 'Wolfgang Bauer'
Subject: Referee report on your article

Herr Bauer, I got the referee report on your article, although the referee did not used the form we provided, the recommendation is to accept the paper provided you incorporate the recommendations listed below.

 

I ask you to please modify your paper and send me a revised version.

 

I thank you ahead of time for your prompt answer.

 

Best wishes . . . Jorge

 

Jorge A. López

Chair and Shumaker professor

Physics Dept., UTEP

915-747-7528

http://jorgelopez.utep.edu/JorgeNYT/jorge.html

 

 

Report on manuscript "Zipf's Law and the Universality Class of the Fragmentation Phase Transition" by W. Bauer, S. Pratt and B. Alleman,

submitted for publication to Acta Phys. Hung.

 

The goal of this work is to study the link between a Zipf's law on the ranking of the clusters and a power law average yield of cluster sizes. This (or closely related problems) has been addressed previously in refs. (a) and (b) cited below and in ref. [15], among others. Following a more complicated reasoning (in particular assuming that the probabilities to have k (small) clusters in a given event are Poissonian, which is not necessary), the authors calculate the probability that a cluster of given size is the largest one (eq. (9)) and the same for the second biggest (eq. (11)). This part of the paper is very detailed and easy to follow (notice some misprints quoted below). In contrast, a big jump is made when claiming on top of page 5 that "If one uses an expansion for our analytical results, one finds that the average cluster size as a function of rank r follows a more general Zipf-Mandelbrot distribution...". It is not clear how one goes from r=2 to a general formula.  In addition, because this result is in disagreement with the above mentioned works (in which a "generalized Zipf's law, with lambda given by the same eq. (13) is found):

i) The derivation of equ. (12) and (13) should be presented.

ii) The reasons of the discrepancies with previous works should be explained.

iii) The values of lambda reported on bottom of page 4 show large deviations with respect to the predictions of eq. (13). Why ?

 

Because Zipf's law is becoming a popular tool for some experimental groups working in nuclear fragmentation, I believe it is important to clearly explain why this method of analysis is not bringing any new information. This message should appear more strongly in the paper.

 

- On top of page 3 one should read "...of size A is <N(A)>=..."

- In equation (8), the exponential should be exp(-<N(i)> and n! should be k!

- In equation (9), the last exponential should be exp(-[....])

- In figure. 3 (left), one should replace t=2 by tau=2

- In the caption of figure 3, the last sentence is: "Dashed line: asymptotic

  expansion of equation 13". I do not understand what means an asymptotic

  expansion of this equation. 

- Ref. [15] has been published in Phys. Rev. C72, 057602(2005).

 

(a) J. Bouchaud and M. Potters, in Theory of Financial Risk and Derivative Pricing, page 19, Cambridge University Press, 2nd edition, (2003).

(b) M. Newman, Contemporary Physics, 46, 323 (2005).

(c) L. A. Adamic, www.hpl.hp.com/research/idl/papers/ranking/ranking.html.