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Coupled dynamics of fast spins and slow interactions in neural networks and spin systems

R W Penney, A C C Coolen and D Sherrington

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The authors examine an Ising spin system in which both spins and the interactions between them may evolve in time, although on disparate timescales, such that the couplings change adiabatically. In thermal equilibrium they find a novel application of the replica method, but for finite replica number, representing the ratio of the temperatures of the spin and interaction systems. Regimes where the motion of the couplings has non-trivial effects are found in addition to those where solely the stochasticity of these interaction weights in significant, and this issue is closely related to the orders of the transitions between the various phases observed. Simulation results lend support to the analysis.


PACS

07.05.Mh Neural networks, fuzzy logic, artificial intelligence

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)

75.10.Hk Classical spin models

MSC

82C26 Dynamic and nonequilibrium phase transitions (general)

82C32 Neural nets (See also 68T05, 91E40, 92B20)

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

Subjects

Condensed matter: electrical, magnetic and optical

Instrumentation and measurement

Statistical physics and nonlinear systems

Dates

Issue 15 (7 August 1993)



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