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Persistence properties of a system of coagulating and annihilating random walkers
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UNSPECIFIED (2003) Persistence properties of a system of coagulating and annihilating random walkers. PHYSICAL REVIEW E, 68 (4 Part 2). . doi:10.1103/PhysRevE.68.046103 ISSN 1063651X.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.68.046103
Abstract
We study a ddimensional system of diffusing particles that on contact either annihilate with probability 1/(q1) or coagulate with probability (q2)/(q1). In one dimension, the system models the zerotemperature Glauber dynamics of domain walls in the qstate Potts model. We calculate (P) over bar (m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m1) coagulations. Using perturbative renormalization group analysis for d<2, we show that, if the number of coagulations m is much less than the typical number M(t), then (P) over bar (m,t)similar tom(zeta/d)t(theta), with theta=dQ+Q(Q1/2)epsilon+O(epsilon(2)), zeta=(2Q1)epsilon+(2Q1)(Q1)(1/2+AQ)epsilon(2)+O(epsilon(3)), where Q=(q1)/q, epsilon=2d and A=0.006.... M(t) is shown to scale as M(t)similar tot(d/2delta), where delta=d(1Q)+(Q1)(Q1/2)epsilon+O(epsilon(2)). In two dimensions, we show that (P) over bar (m,t)similar toln(t)(Q(32Q))ln(m)((2Q1)2)t(2Q) for m<t(2Q1). We also derive an exact nonperturbative relation between the exponents: namely delta(Q)=theta(1Q). The onedimensional results corresponding to epsilon=1 are compared with results from Monte Carlo simulations.
Item Type:  Journal Article  

Subjects:  Q Science > QC Physics  
Journal or Publication Title:  PHYSICAL REVIEW E  
Publisher:  AMERICAN PHYSICAL SOC  
ISSN:  1063651X  
Official Date:  October 2003  
Dates: 


Volume:  68  
Number:  4 Part 2  
Number of Pages:  12  
Page Range:    
DOI:  10.1103/PhysRevE.68.046103  
Publication Status:  Published 
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