Duality in Finite-Dimensional Spin Glasses |
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Authors: | Hidetoshi Nishimori |
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Affiliation: | (1) Department of Physics, Tokyo Institute of Technology, Tokyo, Japan |
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Abstract: | We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function. |
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