Complex and Non-Complex Phase Structures in Models of Spin Glasses and Information Processing

Details Complex and Non-Complex Phase Structures in Models of Spin Glasses and Information Processing Complex and Non-Complex Phase Structures in Models of Spin Glasses and Information Processing

2002-01-09

arxiv.org/abs/cond-mat/0201121v1

Physica A 315 (2002) 243-254

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 pages; Proceedings of the International Symposium on Slow Dynamics in Nature, Seoul, Korea, November 2001; to be published

Scientific paper

10.1016/S0378-4371(02)01228-1

The gauge theory of spin glasses and statistical-mechanical formulation of error-correcting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation functions and on the distribution functions of order parameters. These functional identities restrict the possibilities of slow dynamics and complex structure of the phase space. An inequality for error-correcting codes is shown to be interpreted to indicate non-monotonicity of spin orientation as a function of the temperature in spin glasses.

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