Analysis of an Extended +-J Ising Spin Glass Model by Using a Gauge Symmetry

Details Analysis of an Extended +-J Ising Spin Glass Model by Using a Gauge Symmetry Analysis of an Extended +-J Ising Spin Glass Model by Using a Gauge Symmetry

2011-08-04

arxiv.org/abs/1108.1117v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, no figures. v2: minor corrections/additions

Scientific paper

We investigate an extended +-J Ising spin glass model by using a gauge symmetry. This model has +-J1 interactions and +-J2 interactions. We show that a gauge symmetry is usable to study this model. The exact internal energy, the rigorous upper bound of the specific heat and some rigorous relations for correlation functions and order parameters are shown by using the gauge symmetry. Also a part of our results, e.g., the value of the exact internal energy should be useful for checking the computer programs for investigating this model. In addition, we find that the present solutions are generalized solutions which include the solutions for the conventional +-J Ising spin glass model and the solutions for the bond-diluted +-J Ising spin glass model. The solutions for the conventional +-J Ising spin glass model are the solutions on the so-called Nishimori line. Moreover, we discuss the locations of the transition temperatures on the square lattice. We conclude that this model has not a finite-temperature spin glass transition for the symmetric distribution of randomness. We obtain the equations which give precise but approximate locations of the multicritical points for this model and the bond-diluted +-J Ising spin glass model.

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