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Numerical study of the critical properties of an irreversible cellular automaton

Yu He, Kan Chen, C. Jayaprakash

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Abstract

We have studied the critical properties of an irreversible cellular automaton using numerical renormalization-group and finite-size scaling methods. We have determined the values of the correlation-length exponent $\ensuremath{\nu}$ and an appropriately defined dynamic scaling exponent $z$. Our values are consistent with those of the kinetic Ising model. This provides numerical support for the result that continuous ferromagnetic transitions in irreversible systems belong in the same universality class as that of the Ising model.

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What this paper is about

We have studied the critical properties of an irreversible cellular automaton using numerical renormalization-group and finite-size scaling methods. We have determined the values of the correlation-length exponent $\ensuremath{\nu}$ and an appropriately defined dynamic scaling exponent $z$. Our values are consistent with those of the kinetic Ising model. This provides numerical support for the result that continuous ferromagnetic transitions in irreversible systems belong in the same universality class as that of the Ising model.

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Available abstract

We have studied the critical properties of an irreversible cellular automaton using numerical renormalization-group and finite-size scaling methods. We have determined the values of the correlation-length exponent $\ensuremath{\nu}$ and an appropriately defined dynamic scaling exponent $z$. Our values are consistent with those of the kinetic Ising model. This provides numerical support for the result that continuous ferromagnetic transitions in irreversible systems belong in the same universality class as that of the Ising model.

Key concepts: Renormalization group, Ising model, Critical exponent, Scaling, Statistical physics, Exponent, Universality (dynamical systems), Cellular automaton

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