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Kinetic Ising model in two and three dimensions with constraints
Author(s) -
Kuhlmann Claudia,
Trimper Steffen,
Schulz Michael
Publication year - 2005
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200440092
Subject(s) - ising model , autocorrelation , exponent , arrhenius equation , kinetic energy , statistical physics , relaxation (psychology) , spins , exponential function , physics , activation energy , exponential decay , coupling (piping) , monte carlo method , condensed matter physics , chemistry , materials science , kinetics , quantum mechanics , mathematics , psychology , social psychology , linguistics , statistics , philosophy , mathematical analysis , metallurgy
We present the dynamics of the kinetically constrained Ising model, comprised of a system of spins coupled with the strength J and situated in a field which plays the role of activation energy. Due to kinetic constraints, glassy effects arise at low temperatures leading to a non‐Arrhenius α ‐relaxation time. The results of Monte Carlo simulations are presented for the 2D and 3D facilitated kinetic Ising model with nonzero coupling J . The spin autocorrelation function exhibits, in a broad intermediate time regime, a pronounced stretched exponential decay characterized by an exponent γ . Whereas the relaxation time depends strongly on the activation energy and the interaction strength J , we find a non‐universal stretching exponent γ depending on the temperature and on J . In 3D the autocorrelation function shows a crossover into a pure exponential decay consistent with theoretical predictions. The magnetization is also analyzed and identified as a control parameter of the system. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)