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

Abstract

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 $1/2\le s\le 1$. 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.

5+1 pages. v2: published version

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Cited by in corpus (4)

• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• RG studies of scalar-field models of long-range interactions
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Criticality in 1-dimensional field theories with mesoscopic, infinite range interactions