New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature

Maria Chiara Angelini; Carlo Lucibello; Giorgio Parisi; Federico Ricci-Tersenghi; Tommaso Rizzo

doi:10.1073/pnas.1909872117

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arXiv · 1906.04437

New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature

Maria Chiara Angelini·Carlo Lucibello·Giorgio Parisi·Federico Ricci-Tersenghi·Tommaso Rizzo

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Abstract

We apply to the Random Field Ising Model at zero temperature (T= 0) the perturbative loop expansion around the Bethe solution. A comparison with the standard epsilon-expansion is made, highlighting the key differences that make the new expansion much more appropriate to correctly describe strongly disordered systems, especially those controlled by a T = 0 RG fixed point. This new loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding new terms that are absent in the epsilon-expansion. However, these new terms are subdominant with respect to the standard, supersymmetric ones, therefore dimensional reduction is still valid at this order of the loop expansion.

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Maria Chiara Angelini, Carlo Lucibello, Giorgio Parisi, Federico Ricci-Tersenghi, Tommaso Rizzo. 2019-06-11. New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature. https://doi.org/10.1073/pnas.1909872117

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