Mean field, long-range ferromagnets and periodic boundary conditions

Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions

Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a 1/r law, are discussed in the mean field approximation.

Dilution Robustness for Mean Field Ferromagnets

In this work we compare two different random dilutions on a mean field ferromagnet: the first model is built on a Bernoulli-diluted graph while the second lives on a Poisson-diluted one. While it is known that the two models have, in the thermodynamic limit, the same free energy, we investigate on the structural constraints that the two models must fulfill. We rigorously derive for each model t...

Evidence against a Mean Field Description of Short-Range Spin Glasses Revealed through Thermal Boundary Conditions

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Duality in Long-Range Ising Ferromagnets

It is proved that for a system of spins σi = ±1 having an interaction energy − ∑ Kijσiσj with all theKij strictly positive, one can construct a dual formulation by associating a dual spin Sijk = ±1 to each triplet of distinct sites i, j and k. The dual interaction energy reads − ∑

Perturbation of Periodic Boundary-Conditions