1d Ising model with $1/r^{1.99}$ interaction

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Benedetti, Dario, Lauria, Edoardo, Mazáč, Dalimil, van Vliet, Philine
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908380980838400
author Benedetti, Dario
Lauria, Edoardo
Mazáč, Dalimil
van Vliet, Philine
author_facet Benedetti, Dario
Lauria, Edoardo
Mazáč, Dalimil
van Vliet, Philine
contents We study the 1d Ising model with long-range interactions decaying as $1/r^{1+s}$. The critical model corresponds to a family of 1d conformal field theories (CFTs) whose data depends nontrivially on $s$ in the range $1/2\leq s\leq 1$. The model is known to be described by a generalized free field with quartic interaction, which is weakly coupled near $s=1/2$ but strongly coupled near the short-range crossover at $s=1$. We propose a dual description which becomes weakly coupled at $s=1$. At $s=1$, our model becomes an exactly solvable conformal boundary condition for the 2d free scalar. We perform a number of consistency checks of our proposal and calculate the perturbative CFT data around $s=1$ analytically using both 1) our proposed field theory and 2) the analytic conformal bootstrap. Our results show complete agreement between the two methods.
format Preprint
id arxiv_https___arxiv_org_abs_2412_12243
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle 1d Ising model with $1/r^{1.99}$ interaction
Benedetti, Dario
Lauria, Edoardo
Mazáč, Dalimil
van Vliet, Philine
High Energy Physics - Theory
Statistical Mechanics
Mathematical Physics
We study the 1d Ising model with long-range interactions decaying as $1/r^{1+s}$. The critical model corresponds to a family of 1d conformal field theories (CFTs) whose data depends nontrivially on $s$ in the range $1/2\leq s\leq 1$. The model is known to be described by a generalized free field with quartic interaction, which is weakly coupled near $s=1/2$ but strongly coupled near the short-range crossover at $s=1$. We propose a dual description which becomes weakly coupled at $s=1$. At $s=1$, our model becomes an exactly solvable conformal boundary condition for the 2d free scalar. We perform a number of consistency checks of our proposal and calculate the perturbative CFT data around $s=1$ analytically using both 1) our proposed field theory and 2) the analytic conformal bootstrap. Our results show complete agreement between the two methods.
title 1d Ising model with $1/r^{1.99}$ interaction
topic High Energy Physics - Theory
Statistical Mechanics
Mathematical Physics
url https://arxiv.org/abs/2412.12243