Duality in finite-dimensional spin glasses

Details Duality in finite-dimensional spin glasses Duality in finite-dimensional spin glasses

2006-02-20

arxiv.org/abs/cond-mat/0602453v3

J. Stat. Phys. 126 (2007) 977

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 3 figures; A reference added; to appear in J. Stat. Phys

Scientific paper

10.1007/s10955-006-9156-1

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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