R W Penney et al 1993 J. Phys. A: Math. Gen. 26 3681 doi:10.1088/0305-4470/26/15/018
R W Penney, A C C Coolen and D Sherrington
Show affiliationsThe 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.
07.05.Mh Neural networks, fuzzy logic, artificial intelligence
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
Condensed matter: electrical, magnetic and optical
Issue 15 (7 August 1993)
R W Penney et al 1993 J. Phys. A: Math. Gen. 26 3681
A Dimakis et al 1993 J. Phys. A: Math. Gen. 26 1927
B Derrida et al 1993 J. Phys. A: Math. Gen. 26 1493
N Brunel et al 1992 J. Phys. A: Math. Gen. 25 5017
A W Sandvik 1992 J. Phys. A: Math. Gen. 25 3667
Y S Yang and C J Thompson 1991 J. Phys. A: Math. Gen. 24 L279
E B Lin 1991 J. Phys. A: Math. Gen. 24 L1045
M Wilkinson et al 1991 J. Phys. A: Math. Gen. 24 175
V Pasquier 1987 J. Phys. A: Math. Gen. 20 L221
K Svozil 1987 J. Phys. A: Math. Gen. 20 3861