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Scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension

Theoretische Tieftemperaturphysik

Jan 1, 20010 citations

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

D. Zhong, Daniel ben‐Avraham, M. A. Mu�oz

arXiv:cond-mat/0304453The European Physical Journal BOct 1, 20035 citations

Scaling relation for phase transitions in a one-dimensional x-y model

В. И. Пономарев, В. М. Конторович, V. M. Tsukernik

Journal of Experimental and Theoretical PhysicsMar 1, 19740 citations

Absence of absorbing phase transitions in a conserved lattice-gas model in one dimension

Sungchul Kwon, J. M. Kim

A one-dimensional conserved lattice-gas model is known to undergo continuous absorbing phase transitions where some of the critical exponents are exactly known. In one dimension, we recently showed that the model is mapped onto a two species reaction A+B→0 with diffusion rate of D_{A}>0 and D_{B}=0. In this work, it is explicitly shown from the scaling theory for A+B→0 that the observed scaling behavior of the conserved lattice-gas model is not associated with the absorbing phase transitions. Instead, the model indeed undergoes a crossover between two different scaling behaviors of A+B→0, the scaling behaviors of equal and unequal initial densities of two species. The crossover is similar to the absorbing transitions in many respects but some important features of continuous transitions such as the diverging fluctuations of an order parameter are absent.A one-dimensional conserved lattice-gas model is known to undergo continuous absorbing phase transitions where some of the critical exponents are exactly known. In one dimension, we recently showed that the model is mapped onto a two species reaction A+B→0 with diffusion rate of D_{A}>0 and D_{B}=0. In this work, it is explicitly shown from the scaling theory for A+B→0 that the observed scaling behavior of the conserved lattice-gas model is not associated with the absorbing phase transitions. Instead, the model indeed undergoes a crossover between two different scaling behaviors of A+B→0, the scaling behaviors of equal and unequal initial densities of two species. The crossover is similar to the absorbing transitions in many respects but some important features of continuous transitions such as the diverging fluctuations of an order parameter are absent.

Physical review. EJan 7, 20163 citations

Scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension

S. Lübeck

We analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field [Phys. Rev. Lett. 85, 1803 (2000)]. We determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in D=2,3,4,5 dimensions. A comparison of our results and those obtained from a mean-field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four.We analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field [Phys. Rev. Lett. 85, 1803 (2000)]. We determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in D=2,3,4,5 dimensions. A comparison of our results and those obtained from a mean-field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four.

arXiv:cond-mat/0104451Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 22, 200144 citations

Scaling behavior of the order parameter and its conjugated field in an absorbing phase transition around the upper critical dimension

S. Lübeck

We analyze numerically the critical behavior of an absorbing phase transition in a conserved lattice gas in an external field. The external field is realized as a spontaneous creation of active particles that drives the system away from criticality. Nevertheless, the order parameter obeys certain scaling laws for sufficiently small external fields. These scaling laws are investigated and the corresponding exponents are determined in various dimensions (D=2,3,4,5). At the so-called upper critical dimension D(c)=4 one has to modify the usual scaling laws by logarithmic corrections.We analyze numerically the critical behavior of an absorbing phase transition in a conserved lattice gas in an external field. The external field is realized as a spontaneous creation of active particles that drives the system away from criticality. Nevertheless, the order parameter obeys certain scaling laws for sufficiently small external fields. These scaling laws are investigated and the corresponding exponents are determined in various dimensions (D=2,3,4,5). At the so-called upper critical dimension D(c)=4 one has to modify the usual scaling laws by logarithmic corrections.

arXiv:cond-mat/0202014Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsApr 12, 200232 citations

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

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