Duality in finite-dimensional spin glasses
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.
Keywords
Cite
@article{arxiv.cond-mat/0602453,
title = {Duality in finite-dimensional spin glasses},
author = {Hidetoshi Nishimori},
journal= {arXiv preprint arXiv:cond-mat/0602453},
year = {2007}
}
Comments
12 pages, 3 figures; A reference added; to appear in J. Stat. Phys