Francesco Chippari, Marco Picco, Raoul Santachiara
SciPost Phys. 15, 135 (2023) ·
published 4 October 2023

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In this paper we provide new analytic results on twodimensional $q$Potts models ($q ≥ 2$) in the presence of bond disorder correlations which decay algebraically with distance with exponent $a$. In particular, our results are valid for the longrange bond disordered Ising model ($q=2$). We implement a renormalization group perturbative approach based on conformal perturbation theory. We extend to the longrange case the RG scheme used in [V. Dotsenko et al., Nucl. Phys. B 455 70123] for the shortrange disorder. Our approach is based on a $2$loop order double expansion in the positive parameters $(2a)$ and $(q2)$. We will show that the WeinribHalperin conjecture for the longrange thermal exponent can be violated for a nonGaussian disorder. We compute the central charges of the longrange fixed points finding a very good agreement with numerical measurements.
Nina Javerzat, Sebastian Grijalva, Alberto Rosso, Raoul Santachiara
SciPost Phys. 9, 050 (2020) ·
published 12 October 2020

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We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a oneparameter ($H$) family of percolation models with longrange correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $\frac{3}{4}<H< 0$ instead, there is a line of critical points with continously varying exponents. The universality class of these points, in particular concerning the conformal invariance of the level clusters, is poorly understood. By combining the Conformal Field Theory and the numerical approach, we provide new insights on these phases. We focus on the connectivity function, defined as the probability that two sites belong to the same level cluster. In our simulations, the surfaces are defined on a lattice torus of size $M\times N$. We show that the topological effects on the connectivity function make manifest the conformal invariance for all the critical line $H<0$. In particular, exploiting the anisotropy of the rectangular torus ($M\neq N$), we directly test the presence of the two components of the traceless stressenergy tensor. Moreover, we probe the spectrum and the structure constants of the underlying Conformal Field Theory. Finally, we observed that the corrections to the scaling clearly point out a breaking of integrability moving from the pure percolation point to the longrange correlated one.
SciPost Phys. 7, 044 (2019) ·
published 7 October 2019

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We perform MonteCarlo computations of fourpoint cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to fourpoint functions in a CFT that interpolates between Dseries minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT fourpoint functions, down to the $2$ to $4$ significant digits of our MonteCarlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the halfplane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.
SciPost Phys. 1, 009 (2016) ·
published 27 October 2016

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We study fourpoint functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and nondiagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute fourpoint functions using a numerical conformal bootstrap approach. The results agree with MonteCarlo computations of connectivities of random clusters.
Commentaries
Commentaries for which this Contributor is identified as an author:
Liouville theory with a central charge less than one
by Sylvain Ribault, Raoul Santachiara · http://arxiv.org/abs/1503.02067v2
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