2005/01/17 by Koujin Takeda, Tomohiro Sasamoto, Hidetoshi Nishimori
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/17/004
published as J.Phys. A38 (2005) 3751-3774 · 27 pages, 3 figures
arxiv created 2005/01/17 · openalex publication_date 2005/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulas which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self dual cases, in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices. The examples include the +-J and Gaussian Ising spin glasses on the square, hexagonal and triangular lattices, the Potts and Zq models with chiral randomness on these lattices, and the three-dimensional +-J Ising spin glass and the random plaquette gauge model.