### Abstract

Original language | English |
---|---|

Pages (from-to) | 4514-4523 |

Number of pages | 10 |

Journal | Physical Review B: Condensed Matter and Materials Physics |

Volume | 42 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Sep 1990 |

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### Cite this

*Physical Review B: Condensed Matter and Materials Physics*,

*42*(7), 4514-4523. https://doi.org/10.1103/PhysRevB.42.4514

}

*Physical Review B: Condensed Matter and Materials Physics*, vol. 42, no. 7, pp. 4514-4523. https://doi.org/10.1103/PhysRevB.42.4514

**Growth of order in vector spin systems and self-organized criticality.** / Newman, T. J.; Bray, A. J.; Moore, M. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Growth of order in vector spin systems and self-organized criticality

AU - Newman, T. J.

AU - Bray, A. J.

AU - Moore, M. A.

PY - 1990/9/1

Y1 - 1990/9/1

N2 - We consider the process of zero-temperature ordering in a vector-spin system, with nonconserved order parameter (model A), following an instantaneous quench from infinite temperature. We present the results of numerical simulations in one spatial dimension for spin dimension n in the range 2n5. We find that a scaling regime [where a characteristic-length scale L(t) emerges] is entered in all cases for sufficiently long times with L(t)t1/2 for n3 and L(t)t1/4 for n=2. The autocorrelation function A(t) is found to decay with time as A(t)t-(1-)/2 for n3, where is a new n-dependent exponent at the T=0 fixed point (as predicted in a recent 1/n expansion). For n=2, A(t) exp(-at1/2). We give simple analytical arguments explaining the anomalous behavior found for n=2. We also discuss the new exponents at the T=0 fixed point in the wider context of self-organizing systems.

AB - We consider the process of zero-temperature ordering in a vector-spin system, with nonconserved order parameter (model A), following an instantaneous quench from infinite temperature. We present the results of numerical simulations in one spatial dimension for spin dimension n in the range 2n5. We find that a scaling regime [where a characteristic-length scale L(t) emerges] is entered in all cases for sufficiently long times with L(t)t1/2 for n3 and L(t)t1/4 for n=2. The autocorrelation function A(t) is found to decay with time as A(t)t-(1-)/2 for n3, where is a new n-dependent exponent at the T=0 fixed point (as predicted in a recent 1/n expansion). For n=2, A(t) exp(-at1/2). We give simple analytical arguments explaining the anomalous behavior found for n=2. We also discuss the new exponents at the T=0 fixed point in the wider context of self-organizing systems.

UR - http://www.scopus.com/inward/record.url?scp=0000836291&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.42.4514

DO - 10.1103/PhysRevB.42.4514

M3 - Article

AN - SCOPUS:0000836291

VL - 42

SP - 4514

EP - 4523

JO - Physical Review B: Condensed Matter and Materials Physics

JF - Physical Review B: Condensed Matter and Materials Physics

SN - 1098-0121

IS - 7

ER -