Phys. Rev. Lett. 75, 3210–3213 (1995)Universality in Random-Walk Models with Birth and DeathReceived 6 June 1995; published in the issue dated 30 October 1995 Models of random walks are considered in which walkers are born at one site and die at all other sites. Steady-state distributions of walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D≠2, 4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. This work elucidates the adsorption transition of polymers at curved interfaces. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.75.3210
DOI:
10.1103/PhysRevLett.75.3210
PACS:
05.50.+q, 05.20.-y, 05.40.+j
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