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

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 - https://www.scopus.com/pages/publications/0000836291

U2 - 10.1103/PhysRevB.42.4514

DO - 10.1103/PhysRevB.42.4514

M3 - Article

AN - SCOPUS:0000836291

SN - 1550-235X

VL - 42

SP - 4514

EP - 4523

JO - Physical Review B: Condensed matter and materials physics

JF - Physical Review B: Condensed matter and materials physics

IS - 7

ER -