2005 Fiscal Year Final Research Report Summary
Statistical mechanical study of disordered systems by the method of stochastic information processing
| Project/Area Number |
14084205
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
NISHIMORI Hidetoshi Tokyo Institute of Technology, Physics, Professor, 大学院理工学研究科, 教授 (70172715)
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| Co-Investigator(Kenkyū-buntansha) |
SASAMOTO Tomohiro Chiba University Mathematics, Associate Professor, 理学部, 助教授 (70332640)
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| Project Period (FY) |
2002 – 2005
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| Keywords | spin glass / error correcting codes / limit of error correction |
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| Research Abstract |
We first summarized previous knowledge in classical information science with an eye on the relation between error correcting codes and the theory of spin glasses, hoping to clarify how the results in information science are interpreted in the context of spin glasees. Based on this study, we have clarified the difference in the importance from the view point of information science and the significance as spin glass theory. For example, channel coding formulated by Shannon gives the condition for decoding to be successful, whereas, if interpreted in the context of the theory of spin glasses, the same theorem yields the condition for the perfect ferromagnetic phase to exist Decoding of noisy signal loses its significance unless the decoded message is in perfect agreement with the original message; but in the physics of magnetism non-maximum values of magnetization are of course physically prevalent.
We have also studied the competition between quantum effects and randomness in spin systems by solving an infinite-range model. The result shows that quantum effects are not very significant in qualitative determination of the structure of the phase diagram. Nevertheless we observed many typical critical phenomena in the low-temperature phase of this model, which suggests that competition of randomness and frustration, without quantum effects, causes many non-trivial phenomena. We have further presented a conjecture on the exact location of the multicritical point of finite-dimensional spin glasses.
We have derived the limit of noise strength above which error correction becomes impossible in toric code, a quantum memory, by exploiting the formal relation between the spin glass theory and quantum error correction. We have generalized this conjecture to non-self dual cases, thus yielding the correction limit for torus code with time dependence in error detection.
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