Mean Field Dilute Ferromagnet: High Temperature and Zero Temperature Behavior |
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Authors: | Luca De Sanctis Francesco Guerra |
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Institution: | (1) Dipartimenti di Matematica e Psicologia, Università di Bologna, P.zza di Porta San Donato 5, 40126 Bologna, Italy;(2) Dipartimento di Fisica, Sapienza Università di Roma, and INFN, sezione di Roma1, P.le Aldo Moro 2, 00185 Roma, Italy |
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Abstract: | We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high
temperature, and at temperature zero. We find the critical line of the model, separating the phase with zero magnetization
from the phase with symmetry breaking. We also compute exactly the entropy at temperature zero, which is strictly positive.
The physical behavior at temperature zero is very interesting and related to infinite dimensional percolation, and suggests
possible behaviors at generic low temperatures. Lastly, we provide a complete solution for a (partially) annealed model. Our
results hold both for the Poisson and the Bernoulli versions of the model. |
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Keywords: | Mean field Dilute ferromagnet Interpolation techniques Convexity methods |
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