A non-conserving coagulation model with enhanced activity of small masses

A coagulation process is studied in a set of random masses, in which two randomly chosen masses and the smallest mass of the set multiplied by some fixed parameter γ ∈ [−1, 1] are iteratively added. Besides masses (or primary variables), secondary variables are also considered that are correlated with primary variables and coagulate according to the above rule with γ = 0. This process interpolates between known statistical physical models: The case γ = −1 corresponds to the strong disorder renormalization group transformation of certain disordered quantum spin chains whereas γ = 1 describes coarsening in the one-dimensional Glauber-Ising model. The case γ = 0 is related to the renormalization group transformation of a recently introduced graph with a fat-tail edge-length distribution. In the intermediate range −1 < γ < 1, the exponents αγ and βγ that describe the growth of the primary and secondary variable, respectively, are accurately estimated by analyzing the differential equations describing the process in the continuum formulation. According to the results, the exponent αγ varies monotonously with γ while βγ has a maximum at γ = 0. PACS numbers: 05.40.-a, 68.43.Jk, 05.10.Cc A non-conserving coagulation model with enhanced activity of small masses 2