NUTZEL, K and KREY, U (1993) SUBTLE DYNAMIC BEHAVIOR OF FINITE-SIZE SHERRINGTON-KIRKPATRICK SPIN-GLASSES WITH NONSYMMETRICAL COUPLINGS. [["eprint_typename_letter" not defined]]
Full text not available from this repository.Abstract
We have studied numerically the parallel dynamics of non-symmetric Sherrington-Kirkpatrick spin glasses, varying the degree of symmetry eta := [J(i,k)J(k,i)]/[J(i,k)2] of the coupling coefficients between 0 and 1. For systems of finite size N, in the limit t --> infinity and at 'zero temperature', T = 0, we find subtle behaviour of the function [C2(t)] := [s(i)(t - 1)s(i)(t + 1)], which characterizes the appearance of 2-cycles or fixed-point attractors quantitatively. One has to distinguish the two cases eta > 0.5, where [C2(infinity)] --> 1, i.e. the system is eventually trapped with probability 1 in a fixed-point or a 2-cycle, if after t --> infinity the limit N --> infinity is taken, and eta < 0.5, where, in contrast, [C2(infinity)]is < 1, since longer cycles appear. However, the 'trapping' for eta > 0.5 happens only for T = 0, and at time scales tau(N) which increase exponentially with N, whereas for T > 0, or if for T = 0 the limit N --> infinity would be taken before t --> infinity, the quantity (C2(t --> infinity)) would decrease smoothly and monotonically with decreasing eta right from eta = 1, in quantitative agreement with the mean-field simulation of Eissfeller and Opper. For T = 0, the transient behaviour of (C2(t)) between the mean-field value, which is reached already after typically 100 time steps, and the trapping event, is found to be to be governed by log-normal statistics with size-depending parameters.
| Item Type: | ["eprint_typename_letter" not defined] |
|---|---|
| Uncontrolled Keywords: | ASYMMETRIC SK-MODEL; DETERMINISTIC DYNAMICS; GLAUBER DYNAMICS; ATTRACTORS; SYSTEMS; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:42 |
| URI: | https://pred.uni-regensburg.de/id/eprint/53879 |
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