The Lee-Yang model and its generalizations through the lens of long-range deformations

TL;DR

This paper investigates the long-range deformations of the Lee-Yang model and related minimal models, revealing inconsistencies for models with m>2 and establishing an analogy between the m=2 case and the long-range Ising model.

Contribution

It provides a perturbative analysis of long-range deformations of minimal models, highlighting the special case of the Lee-Yang model and its relation to the long-range Ising model.

Findings

Inconsistencies found for m>2 in relating minimal model and Landau-Ginzburg constructions.

The m=2 case (Lee-Yang model) is analogous to the long-range Ising model.

Abstract

In two dimensions, the non-unitary class of conformal minimal models, $\mathcal{M}(2,2m+1)$, has been recently conjectured to arise as renormalization-group fixed points of scalar field theories with complex $i\varphi^{2m-1}$ interaction, $m\in \mathbb{N}$, $m\ge2$. We test a variation of this conjecture through the perturbative study of two separate long-range constructions based on respectively the minimal model and its potential Landau-Ginzburg formalism. For $m>2$, inconsistencies are found when subsequently relating both constructions. In contrast, the long-range Lee-Yang model, the $m=2$ case, is shown to be analogue to the long-range Ising model.