Koujin Takeda et al 2005 J. Phys. A: Math. Gen. 38 3751 doi:10.1088/0305-4470/38/17/004
Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture
Koujin Takeda, Tomohiro Sasamoto and Hidetoshi Nishimori
Show affiliationsWe 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 formulae 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.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Fh Phase transitions: general studies
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B26 Phase transitions (general)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
- Subjects
- Dates
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Issue 17 (29 April 2005)
Received 17 January 2005, in final form 18 January 2005
Published 13 April 2005
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Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture
Koujin Takeda et al 2005 J. Phys. A: Math. Gen. 38 3751
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