Eur. Phys. J. B 47, 449-457 (2005)
https://doi.org/10.1140/epjb/e2005-00340-y

Zipf's law from a communicative phase transition

INFM udR Roma1, Dip. di Fisica. Università “La Sapienza”, Piazzale A. Moro 5, 00185 Roma, Italy

Corresponding author: ^a ramon@pil.phys.uniroma1.it

Received: 14 April 2005
Revised: 28 July 2005
Published online: 28 October 2005

Abstract

Here we present a new model for Zipf's law in human word frequencies. The model defines the goal and the cost of communication using information theory. The model shows a continuous phase transition from a no communication to a perfect communication phase. Scaling consistent with Zipf's law is found in the boundary between phases. The exponents are consistent with minimizing the entropy of words. The model differs from a previous model [Ferrer i Cancho, Solé, Proc. Natl. Acad. Sci. USA 100, 788–791 (2003)] in two aspects. First, it assumes that the probability of experiencing a certain stimulus is controlled by the internal structure of the communication system rather than by the probability of experiencing it in the `outside' world, which makes it specially suitable for the speech of schizophrenics. Second, the exponent α predicted for the frequency versus rank distribution is in a range where , which may explain that of some schizophrenics and some children, with . Among the many models for Zipf's law, none explains Zipf's law for that particular range of exponents. In particular, two simplistic models fail to explain that particular range of exponents: intermittent silence and Simon's model. We support that Zipf's law in a communication system may maximize the information transfer under constraints.