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Replica Theory and Spin Glasses
Flaviano Morone, Francesco Caltagirone, Elizabeth Harrison +1
These are notes from the lectures of Giorgio Parisi given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithm", that took place in Les…
Anomalous finite size corrections in random field models
Carlo Lucibello, Flaviano Morone, Giorgio Parisi +2
The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous convergence of some thermodynamic quantities to their a…
Finite size corrections to disordered Ising models on Random Regular Graphs
Carlo Lucibello, Flaviano Morone, Giorgio Parisi +2
We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physical…
One-dimensional disordered Ising models by replica and cavity methods
Carlo Lucibello, Flaviano Morone, Tommaso Rizzo
Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimen…