arXiv subjects

Christophe Chatelain

Publications and source records attributed to Christophe Chatelain.

At least 19 recordsLinked to original sources

arXiv2025

Tensor Renormalization-Group study of the surface critical behavior of a frustrated two-layer Ising model

Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin-Teller (AT) universality class, as the $J_1-J_2$ Ising model. In this work, the surface critical behavior is studied numerically by Tensor Renormalization-Group calculations. The Bond-Weight Tensor Renormalization Group algorithm is extended to tackle systems with boundaries. It is observed that the two-fold degeneracy of the surface magnetic scaling dimension of the AT model is lifted in the frustrated two-layer Ising model (F2LIM). The splitting is explained by the breaking of the ${\mathbb Z}_2$-symmetry under spin reversal of a single Ising replica in the F2LIM. The two distinct surface magnetic scaling dimensions $x_1^s$ and $x_2^s$ of the F2LIM satisfies a simple duality relation $x_1^s=1/4x_2^s$.

cond-mat.stat-mech↗

arXiv2024

First-order transition and marginal critical behavior in a novel 2D frustrated Ising model

The phase diagram of a novel two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using Tensor-Network Renormalization-Group techniques. This model can be seen as two anti-ferromagnetic Ising replicas coupled by non-local spin-spin interactions, designed in such a way that the continuum limit matches that of the still debated J1 -J2 model and induces a marginal critical behavior. Our model has the advantage of having more symmetries than the J1 -J2 model and of allowing a more straightforward implementation of Tensor-Network Renormalization-Group algorithms We demonstrate the existence of two transition lines, featuring both first and second-order regimes. In the latter, the central charge and the critical exponents are shown to be compatible with the Ashkin-Teller universality class. This picture is consistent with that given by Monte Carlo simulations of the J1 -J2 model but not with recent studies with Tensor-Network techniques.

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arXiv2024

CTMRG study of the critical behavior of an interacting-dimer model

The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically by means of the Corner Transfer Matrix Renormalization Group algorithm. The critical exponents are known to depend on the chemical potential of vacancies, or monomers. At large average density of the latter, the phase transition becomes of first-order. We compute the scaling dimensions of both order parameter and temperature in the second order regime and compare them with the conjecture that the critical behavior is the same as the Ashkin-Teller model on its self-dual critical line.

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arXiv2022

Numerical evidences of a universal critical behavior of 2D and 3D random quantum clock and Potts models

The random quantum $q$-state clock and Potts models are studied in 2 and 3 dimensions. The existence of Griffiths phases is tested in the 2D case with $q=6$ by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu 3D classical modelswith Monte Carlo simulations. No Griffiths phase is found for the clock model. In contrast, numerical evidences of the existence of Griffiths phases in the random Potts model are given and the Finite Size effects are analyzed. The critical point of the random quantum clock model is then studied by Strong-Disorder Renormalization Group. Despite a chaotic behavior of the Renormalization-Group flow at weak disorder, evidences are given that this critical behavior is governed by the same Infinite-Disorder Fixed Point as the Potts model, independently from the number of states $q$.

cond-mat.dis-nn↗

arXiv2022

Finite-Size Scaling of the majority-voter model above the upper critical dimension

The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension $d=4$, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For $d\ge 5$,the estimates of the exponents are close to the prediction $d/2$ when taking into account the dangerous irrelevant variable at theGaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not $d_c=6$ as claimed in the literature, but $d_c=4$ like the equilibrium Ising model.

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arXiv2021

Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models

The random q-state quantum Potts model is studied on hypercubic lattices in dimensions 2 and 3 using the numerical implementation of the Strong Disorder Renormalization Group introduced by Kovacs and Igl{ó}i [Phys. Rev. B 82, 054437 (2010)]. Critical exponents $ν$, d f and $ψ$ at the Infinite Disorder Fixed Point are estimated by Finite-Size Scaling for several numbers of states q between 2 and 50. When scaling corrections are not taken into account, the estimates of both d f and $ψ$ systematically increase with q. It is shown however that q-dependent scaling corrections are present and that the exponents are compatible within error bars, or close to each other, when these corrections are taking into account. This provides evidence of the existence of a super-universality of all 2D and 3D random Potts models.

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arXiv2020

Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model

Entanglement entropy is a powerful tool to detect continuous, discontinuous and even topological phase transitions in quantum as well as classical systems. In this work, von Neumann and Renyi entanglement entropies are studied numerically for classical lattice models in a square geometry. A cut is made from the center of the square to the midpoint of one of its edges, say the right edge. The entanglement entropies measure the entanglement between the left and right halves of the system. As in the strip geometry, von Neumann and Renyi entanglement entropies diverge logarithmically at the transition point while they display a jump for first-order phase transitions. The analysis is extended to a classical model of non-overlapping finite hard rods deposited on a square lattice for which Monte Carlo simulations have shown that, when the hard rods span over 7 or more lattice sites, a nematic phase appears in the phase diagram between two disordered phases. A new Corner Transfer Matrix Renormalization Group algorithm (CTMRG) is introduced to study this model. No logarithmic divergence of entanglement entropies is observed at the phase transitions in the CTMRG calculation discussed here. We therefore infer that the transitions neither can belong to the Ising universality class, as previously assumed in the literature, nor be discontinuous.

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arXiv2019

Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain

Strong-Disorder Renormalization Group (SDRG), despite being a relatively simple real-space renormalization procedure, provides in principle exact results on the critical properties at the infinite-randomness fixed point of random quantum spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of Matrix Product Operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities of finite chains that are inaccessible to SDRG. In this work, the accuracy of this approach is studied and two simple and fast improvements are proposed. The accuracy on the ground state energy is improved by a factor at least equal to 4 for the random Ising chain in a transverse field. Finally, the proposed algorithms are shown to yield Binder cumulants of the 3-color random Ashkin-Teller chain that are compatible with a second-order phase transition while a first-order one is predicted by the original MPO-RG algorithm.

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arXiv2017

Diverging conductance at the contact between random and pure quantum XX spin chains

A model consisting in two quantum XX spin chains, one homogeneous and the second with random couplings drawn from a binary distribution, is considered. The two chains are coupled to two different non-local thermal baths and their dynamics is governed by a Lindblad equation. In the steady state, a current J is induced between the two chains by coupling them together by their edges and imposing different chemical potentials $μ$ to the two baths. While a regime of linear characteristics J versus $Δ$$μ$ is observed in the absence of randomness, a gap opens as the disorder strength is increased. In the infinite-randomness limit, this behavior is related to the density of states of the localized states contributing to the current. The conductance is shown to diverge in this limit.

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arXiv2016

Infinite disorder and correlation fixed point in the Potts model with correlated disorder

Recent Monte Carlo simulations of the q-state Potts model with a disorder displaying slowly-decaying correlations reported a violation of hyperscaling relation caused by large disorder fluctuations and the existence of a Griffiths phase, as in random systems governed by an infinite-disorder fixed point. New simulations, directly made in the limit of an infinite disorder strength, are presented. The magnetic scaling dimension is shown to correspond to the correlated percola-tion fixed point. The latter is shown to be unstable at finite disorder strength but with a large cross-over length which is not accessible to Monte Carlo simulations.

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arXiv2016

Numerical study of the critical phases of the frustrated Z(5) model

The phase diagram of the $\mathbb{Z}(5)$ spin model is studied numerically on the square lattice by means of the {\sl Density Matrix Renormalization Group}. In the regime where the two nearest-neighbor couplings have opposite signs, a critical phase, not observed in earlier Monte Carlo simulations, is identified. The new phase diagram is in agreement with predictions made by M. den Nijs [{\sl Phys. Rev. B} {\bf 31}, 266 (1985)] but for the $\mathbb{Z}(7)$ model rather than the $\mathbb{Z}(5)$ one. All critical phases are shown to be compatible with a central charge $c=1$. The magnetization scaling dimension displays however a different behavior in the different critical phases.

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arXiv2016

Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger Finite-Size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit.

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arXiv2015

Critical behavior in lattice models with two symmetric absorbing state

We analyze nonequilibrium lattice models with up-down symmetry and two absorbing states by mean-field approximations and numerical simulations in two and three dimensions. The phase diagram displays three phases: paramagnetic, ferromagnetic and absorbing. The transition line between the first two phases belongs to the Ising universality class and between the last two, to the direct percolation universality class. The two lines meet at the point describing the voter model and the size $\ell$ of the ferromagnetic phase vanishes with the distance $\varepsilon$ to the voter point as $\ell\sim\varepsilon$, with possible logarithm corrections in two dimensions.

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arXiv2014

DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model

The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus $Υ_2$ is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with $σ=1/2$ at the two transitions. The predicted universal values of $Υ_2$ are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the high-temperature BKT transition, like the XY model, and shown to take a new universal value at the low-temperature one. Finally, the scaling behavior of magnetization at the low-temperature transition is compatible with $η=1/4$.

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arXiv2014

Stability of the Griffiths phase in the 2D Potts model with correlated disorder

A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D $q$-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, only relatively small lattice sizes could be considered so one can wonder whether this Griffiths phase will not shrink and collapse into a single point, the critical point, as the lattice size is increased to much larger values. In this paper, the 2D eight-state Potts model is numerically studied for four different disorder correlations. It is shown that the Griffiths phase cannot be explained as a simple spreading of local transition temperatures caused by disorder fluctuations. As a consequence, the vanishing of the latter in the thermodynamic limit does not necessarily imply the collapse of the Griffiths phase into a single point. In contrast, the width of the Griffiths phase is controlled by the disorder strength. However, for disorder correlations decaying slower than $1/r$, no cross-over to a more usual critical behavior could be observed as this strength is tuned to weaker values.

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arXiv2014

Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder

The $q$-state Potts model with a long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for $q=2,4,8$ and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic Finite-Size Scaling, in a finite range of temperatures around the self-dual point. The critical exponents are shown to depend on both the temperature and the exponent of the algebraic decay of disorder correlations, but not on the number of states of the Potts model. The mechanism leading to the violation of hyperscaling relations is observed in the entire Griffiths phase.

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arXiv2013

Hyperscaling violation in the 2D 8-state Potts model with long-range correlated disorder

The first-order phase transition of the two-dimensional eight-state Potts model is shown to be rounded when long-range correlated disorder is coupled to energy density. Critical exponents are estimated by means of large-scale Monte Carlo simulations. In contrast to uncorrelated disorder, a violation of the hyperscaling relation $γ/ν=d-2x_σ$ is observed. Even though the system is not frustrated, disorder fluctuations are strong enough to cause this violation in the very same way as in the 3D random-field Ising model. In the thermal sector too, evidence is given for such violation in the two hyperscaling relations $α/ν=d-2x_\varepsilon$ and $1/ν=d-x_\varepsilon$. In contrast to the random field Ising model, at least two hyperscaling violation exponents are needed. The scaling dimension of energy is conjectured to be $x_\varepsilon=a/2$, where $a$ is the exponent of the algebraic decay of disorder correlations.

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arXiv2012

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair-annihilation where each particle interacts at most once throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating-function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both infinite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

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