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Diluted Spin Glass

A diluted spin glass is a disordered spin model with a random number of interactions proportional to its number of spins. One binary-spin model has M_N interactions, where M_N is Poisson with mean alphaN, and random log-weight

-H_N(sigma)=sum_(k=1)^(M_N)theta_k(sigma_(i_(1,k)),...,sigma_(i_(p,k)))+sum_(i=1)^Nh_isigma_i.

The interaction functions, fields, and uniformly sampled indices are independent families. Indices are sampled with replacement. Its partition function uses counting measure on {-1,1}^N.

See also

Poisson Distribution, Replica Symmetry Breaking, Spin Glass, Thermodynamic Pressure

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References

Panchenko, D. and Talagrand, M. "Bounds for Diluted Mean-Fields Spin Glass Models." Probab. Th. Rel. Fields 130, 319-336, 2004. https://doi.org/10.1007/s00440-004-0342-2.

Cite this as:

Weisstein, Eric W. "Diluted Spin Glass." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DilutedSpinGlass.html

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