Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton

Details Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton

2001-02-22

arxiv.org/abs/cond-mat/0102395v1

J. Phys. A: Math. Gen. 34, L279-L287 (2001)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 9 figures, uses IOP style

Scientific paper

10.1088/0305-4470/34/19/103

We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase transition in the directed percolation universality class. Estimates for the stochastic time evolution, phase boundaries and critical exponents can be obtained with high precision. This is possible using only modest numerical effort since the thermodynamic limit can be taken analytically in our approach. We also point out further advantages of the TMRG over other numerical approaches, such as classical DMRG or Monte-Carlo simulations.

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