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

Fanny Eustachon

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.

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

Abstract

In two dimensions, the non-unitary class of conformal minimal models, , has been recently conjectured to arise as renormalization-group fixed points of scalar field theories with complex interaction, , . 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 , inconsistencies are found when subsequently relating both constructions. In contrast, the long-range Lee-Yang model, the case, is shown to be analogue to the long-range Ising model.

Paper Structure

This paper contains 6 sections, 42 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. 2d Long-range Lee-Yang model
  3. Other 2d multicritical models
  4. Discussion
  5. Near Mean Field Theory
  6. Non-unitary minimal models

Figures (3)

  • Figure 1: Schematic summary on the expected universality class of the IR fixed point depending on the value $s$.
  • Figure 2: Numerical values of $\beta_3$ for $m\ge2$, fitted with a polynomial fit (up to $m^{-6}$) for $m\ge 20$. Numerical errors are dominated by the precision of the numerical integration scheme.
  • Figure 3: Correspondence in scaling dimensions of important operators between the long-range $i\varphi^3$-theory near mean field theory (in orange) and $\text{LRMM}_{2,5}(1,2)$ near the short-range end (in blue), with the leading order in perturbation theory sketched near the relevant end.