Entropic Repulsion and Lack of the g-Measure Property for Dyson Models

R Bissacot, EO Endo, ACD van Enter… - … in Mathematical Physics, 2018 - Springer
Abstract We consider Dyson models, Ising models with slow polynomial decay, at low
temperature and show that its Gibbs measures deep in the phase transition region are not g …

[PDF][PDF] Phase transitions in multidimensional long-range random field Ising models

L Affonso, R Bissacot, J Maia - arXiv preprint ArXiv:2307.14150, 2024 - researchgate.net
We extend a recent argument by Ding and Zhuang from nearest-neighbor to long-range
interactions and prove the phase transition in a class of ferromagnetic random field Ising …

Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours

L Affonso, R Bissacot, H Corsini, K Welsch - arXiv preprint arXiv …, 2024 - arxiv.org
Following seminal work by J. Fr\" ohlich and T. Spencer on the critical exponent $\alpha= 2$,
we give a proof via contours of phase transition in the one-dimensional long-range …

Phase Transitions in Ising models: the Semi-infinite with decaying field and the Random Field Long-range

J Maia - arXiv preprint arXiv:2403.04921, 2024 - arxiv.org
In this thesis, we present results on phase transition for two models: the semi-infinite Ising
model with a decaying field, and the long-range Ising model with a random field. We study …

Multidimensional Contours\a la Fr\"{o} hlich-Spencer and Boundary Conditions for Quantum Spin Systems

L Affonso - arXiv preprint arXiv:2310.07946, 2023 - arxiv.org
In this thesis, we present results from the investigation of two problems, one related to the
phase transition of long-range Ising models and the other one associated with the …

Long-range Ising models: Contours, phase transitions and decaying fields

L Affonso, R Bissacot, EO Endo, S Handa - Journal of the European …, 2024 - ems.press
Long-range Ising models: Contours, phase transitions and decaying fields Page 1 © 2024
European Mathematical Society Published by EMS Press J. Eur. Math. Soc. (Online first) DOI …

On Long Range Ising Models with Random Boundary Conditions

EO Endo, ACD van Enter, AL Ny - arXiv preprint arXiv:2405.08374, 2024 - arxiv.org
We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair
interactions decaying with power $2-\alpha $(for $0\leq\alpha< 1$), and prepared with …

Phase Transition in Ferromagnetic state Models: Contours, Long-Range Interactions and Decaying Fields

L Affonso, R Bissacot, G Faria, K Welsch - arXiv preprint arXiv:2410.01234, 2024 - arxiv.org
Using the group structure of the state space of $ q-$ state models and a new definition of
contour for long-range spin-systems in $\mathbb {Z}^ d $, with $ d\geq 2$, a …

Nucleation for one-dimensional long-range Ising models

ACD van Enter, B Kimura, W Ruszel… - Journal of Statistical …, 2019 - Springer
In this note we study metastability phenomena for a class of long-range Ising models in one-
dimension. We prove that, under suitable general conditions, the configuration-1-1 is the …

Phase transitions in low-dimensional long-range random field Ising models

J Ding, F Huang, J Maia - arXiv preprint arXiv:2412.19281, 2024 - arxiv.org
We consider the long-range random field Ising model in dimension $ d= 1, 2$, whereas the
long-range interaction is of the form $ J_ {xy}=| xy|^{-\alpha} $ with $1<\alpha< 3/2$ for $ d …