Marco Picco

Sorbonne Université

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Leticia F. Cugliandolo

Centre National de la Recherche Scientifique

Raoul Santachiara

Université Paris-Saclay

Pierre Pujol

Laboratoire de Physique Théorique

Nicolas Sourlas

Centre National de la Recherche Scientifique

Fèlix Ritort

University of Amsterdam

Vladimir S. Dotsenko

Laboratoire de Physique Théorique et Hautes Energies

Francesco Chippari

Laboratoire de Physique Théorique et Hautes Energies

V. Martı́n-Mayor

Universidad Complutense de Madrid

Nikolaos G. Fytas

University of Essex

Federico Corberi

University of Salerno

Cooperative Institutions

Sorbonne Université

Centre National de la Recherche Scientifique

Laboratoire de Physique Théorique et Hautes Energies

Laboratoire de Physique Théorique

Université Paris Cité

Sapienza University of Rome

École Normale Supérieure - PSL

Istituto Nazionale di Fisica Nucleare, Sezione di Roma I

École Normale Supérieure

Université Paris Sciences et Lettres

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Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

HAL (Le Centre pour la Communication Scientifique Directe) (2019)

Nina Javerzat Marco Picco Raoul Santachiara

Critical point (mathematics)

Chiral Potts curve

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Citations (4)

Long-range quenched bond disorder in the bidimensional Potts model

Journal of Statistical Mechanics Theory and Experiment (2023)

Francesco Chippari Marco Picco Raoul Santachiara

We study the bi-dimensional $q$-Potts model with long-range bond correlated disorder. Similarly to [C. Chatelain, Phys. Rev. E 89, 032105], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for $q=1,2,3$-Potts models for different values of the power-law decaying exponent $a$. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for $q=1$ and $q=2$, we can conjecture the phase diagram for $q\in [1,4]$. In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of $q$ and $a$. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawning the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.

Exponent

10.1088/1742-5468/acc72a

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Citations (7)

Dynamical critical behavior on the Nishimori point of frustrated Ising models

Physical review. E (2024)

Ramgopal Agrawal Leticia F. Cugliandolo Lara Faoro L. B. Ioffe Marco Picco

By considering the quench dynamics of two-dimensional frustrated Ising models through numerical simulations, we investigate the dynamical critical behavior on the multicritical Nishimori point (NP). We calculate several dynamical critical exponents, namely, the relaxation exponent z_{c}, the autocorrelation exponent λ_{c}, and the persistence exponent θ_{c}, after a quench from the high temperature phase to the NP. We confirm their universality with respect to the lattice geometry and bond distribution. For a quench from a power-law correlated initial state to the NP, the aging dynamics are much slower. We also look up the issue of multifractality during the critical dynamics by investigating different moments of the spatial correlation function. We observe a single growth law for all the length scales extracted from different moments, indicating that the equilibrium multifractality at the NP does not affect the dynamics.

Critical point (mathematics)

10.1103/physreve.110.034120

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Connectivities of Potts Fortuin–Kasteleyn clusters and time-like Liouville correlator

Nuclear Physics B (2013)

Marco Picco Raoul Santachiara Jacopo Viti Gesualdo Delfino

Percolation (cognitive psychology)

Chiral Potts curve

10.1016/j.nuclphysb.2013.07.014

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Citations (55)

Statistics of lowest excitations in two dimensional Gaussian spin glasses

arXiv (Cornell University) (2001)

Marco Picco Fèlix Ritort Marta Sales‐Pardo

A detailed investigation of lowest excitations in two-dimensional Gaussian spin glasses is presented. We show the existence of a new zero-temperature exponent lambda describing the relative number of finite-volume excitations with respect to large-scale ones. This exponent yields the standard thermal exponent of droplet theory theta through the relation, theta=d(lambda-1). Our work provides a new way to measure the thermal exponent theta without any assumption about the procedure to generate typical low-lying excitations. We find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal exponent obtained in domain-wall theory showing that MacMillan excitations are not typical.

Exponent

10.48550/arxiv.cond-mat/0106554

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Citations (3)

Random bond Potts model: The test of the replica symmetry breaking

Nuclear Physics B (1998)

Vladimir Dotsenko Vl.S. Dotsenko Marco Picco

Chiral Potts curve

Replica trick

Central charge

10.1016/s0550-3213(98)00183-7

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Citations (18)

Coarsening and percolation in the Ising Model with quenched disorder

Journal of Physics Conference Series (2018)

Ferdinando Insalata Federico Corberi L F Cugliandolo Marco Picco

Through large-scale numerical simulations, we study the phase ordering kinetics of the 2d Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities – the winding angle and the pair-connectedness – we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.

Percolation (cognitive psychology)

Social Connectedness

Directed percolation

10.1088/1742-6596/956/1/012018

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Citations (3)

Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach

arXiv (Cornell University) (2023)

Francesco Chippari Marco Picco Raoul Santachiara

In this paper we provide new analytic results on two-dimensional $q$-Potts models ($q \geq 2$) in the presence of bond disorder correlations which decay algebraically with distance with exponent $a$. In particular, our results are valid for the long-range bond disordered Ising model ($q=2$). We implement a renormalization group perturbative approach based on conformal perturbation theory. We extend to the long-range case the RG scheme used in [V. Dotsenko, Nucl. Phys. B 455 701 23] for the short-range disorder. Our approach is based on a $2$-loop order double expansion in the positive parameters $(2-a)$ and $(q-2)$. We will show that the Weinrib-Halperin conjecture for the long-range thermal exponent can be violated for a non-Gaussian disorder. We compute the central charges of the long-range fixed points finding a very good agreement with numerical measurements.

Exponent

10.21468/scipostphys.15.4.135

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Citations (1)

Renormalisation-group calculation of correlation functions for the 2D random bond Ising and Potts models

Nuclear Physics B (1995)

Vladimir Dotsenko Marco Picco Pierre Pujol

Chiral Potts curve

10.1016/0550-3213(95)00534-y

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Citations (103)

Report on 1607.07224v1

arXiv (Cornell University) (2016)

Marco Picco Sylvain Ribault Raoul Santachiara

We study four-point 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 non-diagonal combination of representations of the Virasoro algebra.Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach.The results agree with Monte-Carlo computations of connectivities of random clusters.

10.21468/scipost.report.27

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Citations (0)