# Non-probabilistic fermionic limit shapes

2 PSPM - Probabilités, statistique, physique mathématique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We study a translational invariant free fermions model in imaginary time, with nearest neighbor and next-nearest neighbor hopping terms, for a class of inhomogeneous boundary conditions. This model is known to give rise to limit shapes and arctic curves, in the absence of the next-nearest neighbor perturbation. The perturbation considered turns out to not be always positive, that is, the corresponding statistical mechanical model does not always have positive Boltzmann weights. We investigate how the density profile is affected by this nonpositive perturbation. We find that in some regions, the effects of the negative signs are suppressed, and renormalize to zero. However, depending on boundary conditions, new crazy regions'' emerge, in which minus signs proliferate, and the density of fermions is not in $[0,1]$ anymore. We provide a simple intuition for such behavior, and compute exactly the density profile both on the lattice and in the scaling limit.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02933352
Contributor : Jean-Marie Stéphan <>
Submitted on : Tuesday, September 8, 2020 - 1:34:21 PM
Last modification on : Monday, June 28, 2021 - 2:26:07 PM

### Identifiers

• HAL Id : hal-02933352, version 1
• ARXIV : 2007.06621

### Citation

Saverio Bocini, Jean-Marie Stéphan. Non-probabilistic fermionic limit shapes. 2020. ⟨hal-02933352⟩

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