Zero-temperature dynamics for the ferromagnetic Ising model on random graphs

Olle Häggström

Physica A: Statistical Mechanics and its Applications, 2002, vol. 310, issue 3, 275-284

Abstract: We consider Glauber dynamics at zero temperature for the ferromagnetic Ising model on the usual random graph model on N vertices, with on average γ edges incident to each vertex, in the limit as N→∞. Based on numerical simulations, Svenson (Phys. Rev. E 64 (2001) 036122) reported that the dynamics fails to reach a global energy minimum for a range of values of γ. The present paper provides a mathematically rigorous proof that this failure to find the global minimum in fact happens for allγ>0. A lower bound on the residual energy is also given.

Keywords: Ising model; Random graph; Glauber dynamics; Local search (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:310:y:2002:i:3:p:275-284

DOI: 10.1016/S0378-4371(02)00797-5

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