Phase transition in the takayasu model with desorption
We study a lattice model where particles carrying different masses diffuse and coalesce upon contact, and also unit masses adsorb to a site with rate q or desorb from a site with nonzero mass with rate p. In the limit p=0 (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power-law tail P(m) approximately m(-tau) for large mass. We show that varying the desorption rate p induces a nonequilibrium phase transition in all dimensions. For fixed q, there is a critical p(c)(q) such that if p<p(c)(q), the steady-state mass distribution, P(m) approximately m(-tau) for large m as in the Takayasu case. For p=p(c)(q), we find P(m) approximately m(-tau(c)) where tau(c) is a new exponent, while for p>p(c)(q), P(m) approximately exp(-m/m(*)) for large m. The model is studied analytically within a mean-field theory and numerically in one dimension.
Majumdar
SN
Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.
Krishnamurthy
S
Barma
M