Guilhem Semerjian and Martin Weigt 2004 J. Phys. A: Math. Gen. 37 5525 doi:10.1088/0305-4470/37/21/003
Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
Guilhem Semerjian1 and Martin Weigt2
Show affiliationsWe discuss analytical approximation schemes for the dynamics of diluted spin models. The original dynamics of the complete set of degrees of freedom is replaced by a hierarchy of equations including an increasing number of global observables, which can be closed approximately at different levels of the hierarchy. We illustrate this method on the simple example of the Ising ferromagnet on a Bethe lattice, investigating the first three possible closures, which are all exact in the long time limit, and which yield more and more accurate predictions for the finite-time behaviour. We also investigate the critical region around the phase transition, and the behaviour of two-time correlation functions. We finally underline the close relationship between this approach and the dynamical replica theory under the assumption of replica symmetry.
- PACS
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
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Issue 21 (28 May 2004)
Received 18 February 2004
Published 12 May 2004
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Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
Guilhem Semerjian and Martin Weigt 2004 J. Phys. A: Math. Gen. 37 5525
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