TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.20.2.029
TI  - A strong-weak duality for the 1d long-range Ising model
PY  - 2026/02/03
UR  - https://scipost.org/SciPostPhys.20.2.029
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 20
IS  - 2
SP  - 029
A1  - Benedetti, Dario
AU  - Lauria, Edoardo
AU  - Mazac, Dalimil
AU  - van Vliet, Philine
AB  - We investigate the one-dimensional Ising model with long-range interactions decaying as $1/r^{1+s}$. In the critical regime, for $1/2 ≤ s ≤ 1$, this system realizes a family of nontrivial one-dimensional conformal field theories (CFTs), whose data vary continuously with $s$. For $s>1$ the model has instead no phase transition at finite temperature, as in the short-range case. In the standard field-theoretic description, involving a generalized free field with quartic interactions, the critical model is weakly coupled near $s=1/2$ but strongly coupled in the vicinity of the short-range crossover at $s=1$. We introduce a dual formulation that becomes weakly coupled as $s \to 1$. Precisely at $s=1$, the dual description becomes an exactly solvable conformal boundary condition of the two-dimensional free scalar. We present a detailed study of the dual model and demonstrate its effectiveness by computing perturbatively the CFT data near $s=1$, up to next-to-next-to-leading order in $1-s$, by two independent approaches: (i) standard renormalization of our dual field-theoretic description and (ii) the analytic conformal bootstrap. The two methods yield complete agreement.
ER  -

@Article{10.21468/SciPostPhys.20.2.029,
	title={{A strong-weak duality for the 1d long-range Ising model}},
	author={Dario Benedetti and Edoardo Lauria and Dalimil Mazac and Philine van Vliet},
	journal={SciPost Phys.},
	volume={20},
	pages={029},
	year={2026},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.20.2.029},
	url={https://scipost.org/10.21468/SciPostPhys.20.2.029},
}