Bond diluted Levy spin-glass model and a new finite-size scaling method to determine a phase transition

Abstract

A spin-glass transition occurs both within and outside of the limits of validity of mean-field theory for a diluted one-dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Using different finite-size scaling methods, evidence for a spin-glass transition is also found for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new method is discussed, which can be exported to systems in a magnetic field.

Keywords:

• spin glasses
• phase transition
• finite-size scaling
• disordered systems
• statistical mechanics
• thermodynamics

Acknowledgements

This work was partially supported by the Ministerio de Ciencia y Tecnología (Spain) through Grant No. FIS2007-60977, and by the Junta de Extremadura (Spain) through Grant No. GRU09038 (partially founded by FEDER).

Notes

Note

1. This can be seen, e.g. in Figure 6 of 12 for ρ = 1.5. In the inset of figure 6, α was erroneously misplaced with δ.