Lee-Yang model from the functional renormalization group

Abstract

We investigate the critical properties of the Lee-Yang model in less than six spacetime dimensions using truncations of the functional renormalization group flow. We give estimates for the critical exponents, study the dependence on the regularization scheme, and show the convergence of our results for increasing size of the truncations in four and five dimensions. While with our truncations it is numerically challenging to approach the three-dimensional case, we provide a simple approximation which allows us to qualitatively study the Lee-Yang model in two and three dimensions, and use it to argue the existence of further nonunitary multicritical theories including one which is relevant for the universality class of the Blume-Capel model.

Leading CFT constraints on multi-critical models in d > 2

“…These are known to interpolate with the unitary minimal models of CFT in d = 2. The sequence of models for m odd enjoys a generalization of parity and is conjectured to interpolate with some non-unitary minimal models in d = 2 [12,13]. While there is no formal proof that scale-invariance implies conformal invariance, we take our results as a pragmatic evidence that conformal invariance could be realized at criticality for the entire sequence of scalar theories that we investigated.…”

“…Another interesting property is that the even models are known to interpolate in d = 2 with the unitary minimal CFTs M(p, p + 1) for p = 1 + m/2, which arise from the representations of the infinite dimensional Virasoro algebra [11]. Similarly, there are speculations [12] pointing at the fact that the non-unitary models might interpolate with the sequence of minimal non-unitary multi-critical theories M(2, m + 2) studied in [13]. This is established for the Lee-Yang case m = 3 [14].…”

“…The well-known upper critical dimension of the Lee-Yang universality class is six. All other unversality classes have purely rational upper critical dimensions, starting from n = 2, which corresponds to the quintic model φ 5 and which has been named Blume-Capel universality class in [12], where it has been argued to correspond to a tricritical phase for a Blume-Capel spin system [27][28][29]. We want to draw the reader's attention to this latter universality class because its upper critical dimension is bigger than three; therefore the model provides a less known, but potentially interesting, non-trivial universality class in three dimensions, and potentially it represents a unique example of a theory that is realized for < 1 in a physically interesting scenario.…”

A functional perspective on emergent supersymmetry

“…The idea of keeping the anomalous dimension fixed when studying the RG stability has been discussed also in [61] for multicritical systems. If instead the anomalous dimension is not kept fixed, we expect that (5.9) can be satisfied with arbitrary accuracy for increasing size of the truncation in the space of all possible operators, as has been observed in [62,63] for the Lee-Yang model. The accuracy with which the superscaling relation is satisfied thus becomes a benchmark test for all our numerical estimates.…”

Functional perturbative RG and CFT data in the $$\epsilon $$ ϵ -expansion

“…2 In Sect. 3 we promote the standard perturbative RG to functional perturbative RG and illustrate the procedure by applying it to the Ising and Lee-Yang [26][27][28][29][30][31][32][33] universality classes. Using the beta functionals for the effective potentials in these two examples, we give general formulas for both the spectrum and the structure constants of the underlying CFTs, and use them to highlight the main novelties of the approach.…”