Analytic and numerical bootstrap for the long-range Ising model
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912456666775552 |
|---|---|
| author | Behan, Connor Lauria, Edoardo Nocchi, Maria van Vliet, Philine |
| author_facet | Behan, Connor Lauria, Edoardo Nocchi, Maria van Vliet, Philine |
| contents | We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02742 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analytic and numerical bootstrap for the long-range Ising model Behan, Connor Lauria, Edoardo Nocchi, Maria van Vliet, Philine High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Lattice We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI. |
| title | Analytic and numerical bootstrap for the long-range Ising model |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2311.02742 |