arXiv subjects

Christophe Chatelain

Publications and source records attributed to Christophe Chatelain.

46 records · Page 3Linked to original sources

arXiv2001

Quenched bond dilution in two-dimensional Potts models

We report a numerical study of the bond-diluted 2-dimensional Potts model using transfer matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random bond case, confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder: dilution, self-dual binary random-bond, self-dual continuous random bond.

cond-mat.dis-nn↗

arXiv2001

Evidence for softening of first-order transition in 3D by quenched disorder

We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional 4-state Potts model which is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.

cond-mat.stat-mech↗

arXiv2000

Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models

We report a transfer matrix study of the random bond $q-$state Potts model in the vicinity of the Ising model $q=2$. We draw attention to a precise determination of magnetic scaling dimensions in order to compare with perturbative results. Universality is checked by the computation of the spin-spin correlation function decay exponent obtained with different types of probability distributions of the coupling strengths. Our numerical data, compared to perturbative results for the second moment of the correlation function, obtained with both replica symmetry and replica symmetry breaking schemes, are conclusively in favour of the replica symmetric calculations. The multifractal behaviour of higher moments as well as that of typical correlation functions are also investigated and a comparison is made with the perturbative expansions. Finally, the shape of the correlation function probability distribution is analyzed.

cond-mat.stat-mech↗

arXiv1999

Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries

We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are considered, namely cylinders and square-shaped systems, and the critical behavior is investigated through conformal invariance techniques which were recently shown to be valid, even in the randomness-induced second-order phase transition regime Q>4. In the cylinder geometry, connectivity transfer matrix calculations provide a simple test to find the range of disorder amplitudes which is characteristic of the disordered fixed point. The scaling dimensions then follow from the exponential decay of correlations along the strip. Monte Carlo simulations of spin systems on the other hand are generally performed on systems of rectangular shape on the square lattice, but the data are then perturbed by strong surface effects. The conformal mapping of a semi-infinite system inside a square enables us to take into account boundary effects explicitly and leads to an accurate determination of the scaling dimensions. The techniques are applied to different values of Q in the range 3-64.

cond-mat.stat-mech↗

arXiv1999

Critical Behavior of the Random Potts Chain

We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains ($L \leq 16$) averaging over all possible realizations of disorder configurations chosen according to a binary distribution. Our numerical results show that the critical properties of the model are independent of q in agreement with a renormalization group analysis of Senthil and Majumdar (Phys. Rev. Lett.{\bf 76}, 3001 (1996)). We show how an accurate analysis of moments of the distribution of magnetizations allows a precise determination of critical exponents, circumventing some problems related to binary disorder. Multiscaling properties of the model and dynamical correlation functions are also investigated.

cond-mat.stat-mech↗

arXiv1999

Boundary critical behaviour of two-dimensional random Potts models

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the bulk and at the boundary. Using Monte Carlo techniques the surface and the bulk magnetizations are studied close to the critical temperature and the critical exponents $β_1$ and $β$ are determined. In the strip-like geometry the critical magnetization profile is investigated with free-fixed spin boundary condition and the characteristic scaling dimension, $β_1/ν$, is calculated from conformal field theory. The critical exponents and scaling dimensions are found monotonously increasing with q. Anomalous dimensions of the relevant scaling fields are estimated and the multifractal behaviour at criticality is also analyzed.

cond-mat.stat-mech↗

arXiv1998

Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions

The conformal covariance of correlation functions is checked in the second-order transition induced by random bonds in the two-dimensional 8-state Potts model. The decay of correlations is obtained {\it via} transfer matrix calculations in a cylinder geometry, and large-scale Monte Carlo simulations give access to the correlations and the profiles inside a square with free or fixed boundary conditions, respectively. In both geometries, conformal transformations constrain the form of the spatial dependence, leading to accurate determinations of the order parameter scaling index in good agreement with previous independent determinations obtained through standard techniques. The energy density exponent is also computed.

cond-mat.stat-mech↗

arXiv1998

Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the neighbourhood of the transition point. For strong enough fluctuations of the sequence under consideration, a second-order phase transition is induced. The exponents $β/ν$, $γ/ν$ and $(1-α)/ν$ are obtained at the new fixed point and crossover effects are discussed. Surface properties are also studied.

cond-mat.stat-mech↗

arXiv1998

Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We find that a belonging of the model to the 2D Ising model universality class can be conclusively ruled out, and the dimensions of the relevant bulk and surface scaling fields are found to take the values $y_h=1.849$, $y_t=0.977$, $y_{h_s}=0.54$, to be compared to their Ising values: 15/8, 1, and 1/2.

cond-mat.stat-mech↗

arXiv1997

Aperiodicity-Induced Second-Order Phase Transition in the 8-State Potts Model

We investigate the critical behavior of the two-dimensional 8-state Potts model with an aperiodic distribution of the exchange interactions between nearest-neighbor rows. The model is studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm. The transition point is located through duality relations, and the critical behavior is investigated using FSS techniques at criticality. For strong enough fluctuations of the aperiodic sequence under consideration, a second order phase transition is found. The exponents $β/ν$ and $γ/ν$ are obtained at the new fixed point.

cond-mat.stat-mech↗