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Scaling Relations in Absorbing Phase Transitions with a Conserved Field in One Dimension

Sang-Gui Lee, Sang Bub Lee

Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications EngineeringJan 1, 20090 citations

Phase transition in one dimensional model with unique ground state

Azer Kerimov

Physica A Statistical Mechanics and its ApplicationsMar 1, 19966 citations

Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks

Nóra Menyhárd, Géza Ódor

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are now further investigated numerically, from the point of view of the underlying spin system. Critical exponents characterizing its statics and dynamics are reported. It is found that the influence of the PC transition on the critical exponents of the spins is strong and the origin of drastic changes as compared to the Glauber - Ising case can be traced back to the hyperscaling law stemming from directed percolation. The effect of an external magnetic field, leading to directed percolation-type behaviour on the level of kinks is also studied, mainly via the generalized mean-field approximation.One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are now further investigated numerically, from the point of view of the underlying spin system. Critical exponents characterizing its statics and dynamics are reported. It is found that the influence of the PC transition on the critical exponents of the spins is strong and the origin of drastic changes as compared to the Glauber - Ising case can be traced back to the hyperscaling law stemming from directed percolation. The effect of an external magnetic field, leading to directed percolation-type behaviour on the level of kinks is also studied, mainly via the generalized mean-field approximation.

arXiv:cond-mat/9607089Journal of Physics A Mathematical and GeneralDec 7, 199652 citations

First-Order Phase Transitions in One-Dimensional Steady States

Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg

arXiv:cond-mat/9706114Journal of Statistical PhysicsFeb 1, 199860 citations

Local scale invariance in the parity conserving non-equilibrium kinetic Ising model

Géza Ódor

Local scale invariance has been investigated in the non-equilibrium kinetic Ising model exhibiting an absorbing phase transition of parity conserving type in 1+1 dimensions. Numerical evidence has been found for this symmetry and estimates for the critical ageing exponents are given.

arXiv:cond-mat/0606724Journal of Statistical Mechanics Theory and ExperimentNov 30, 200616 citations

Non-Markovian persistence at the parity conserving point of a one-dimensional nonequilibrium kinetic Ising model

Nóra Menyhárd, Géza Ódor

One-dimensional nonequilibrium kinetic Ising models evolving under the competing effect of spin - flips at zero temperature and nearest-neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent and the exponent characterizing the two-time autocorrelation function of the total magnetization under nonequilibrium conditions are reported. It is found that the critical fluctuations at the PC transition have a strong effect on the spins: the behaviour becomes non-Markovian and the above exponents exhibit drastic changes as compared with the Markovian Glauber - Ising case. In this context the crucial importance of considering the global order parameter (instead of the local one) is emphasized.One-dimensional nonequilibrium kinetic Ising models evolving under the competing effect of spin - flips at zero temperature and nearest-neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent and the exponent characterizing the two-time autocorrelation function of the total magnetization under nonequilibrium conditions are reported. It is found that the critical fluctuations at the PC transition have a strong effect on the spins: the behaviour becomes non-Markovian and the above exponents exhibit drastic changes as compared with the Markovian Glauber - Ising case. In this context the crucial importance of considering the global order parameter (instead of the local one) is emphasized.

arXiv:cond-mat/9706083Journal of Physics A Mathematical and GeneralDec 21, 199714 citations

Mean-field solution of the parity-conserving kinetic phase transition in one dimension

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