arXiv subjects

Andrea Pelissetto

Publications and source records attributed to Andrea Pelissetto.

At least 109 records · Page 6Linked to original sources

arXiv2012

Polymers as compressible soft spheres

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al., Soft Matter 6, 2282 (2010), and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radiiindependent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size.

cond-mat.soft↗

arXiv2012

Coarse-graining strategies in polymer solutions

We review a coarse-graining strategy (multiblob approach) for polymer solutions in which groups of monomers are mapped onto a single atom (a blob) and effective blob-blob interactions are obtained by requiring the coarse-grained model to reproduce some coarse-grained features of the zero-density isolated-chain structure. By tuning the level of coarse graining, i.e. the number of monomers to be mapped onto a single blob, the model should be adequate to explore the semidilute regime above the collapse transition, since in this case the monomer density is very small if chains are long enough. The implementation of these ideas has been previously based on a transferability hypothesis, which was not completely tested against full-monomer results (Pierleoni et al., J. Chem. Phys, 127, 171102 (2007)). We study different models proposed in the past and we compare their predictions to full-monomer results for the chain structure and the thermodynamics in the range of polymer volume fractions Φbetween 0 and 8. We find that the transferability assumption has a limited predictive power if a thermodynamically consistent model is required. We introduce a new tetramer model parametrized in such a way to reproduce not only zero-density intramolecular and intermolecular two-body probabilities, but also some intramolecular three-body and four-body distributions. We find that such a model correctly predicts three-chain effects, the structure and the thermodynamics up to Φ~ 2, a range considerably larger than that obtained with previous simpler models using zero-density potentials. Our results show the correctness of the ideas behind the multiblob approach but also that more work is needed to understand how to develop models with more effective monomers which would allow us to explore the semidilute regime at larger chain volume fractions.

cond-mat.soft↗

arXiv2011

Finite-size scaling in two-dimensional Ising spin glass models

We study the finite-size behavior of two-dimensional spin-glass models. We consider the +-J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of renormalization-group invariant quantities, the overlap susceptibility, and the two-point correlation function confirms that they belong to the same universality class. We analyze in detail the standard finite-size scaling limit in terms of TL^(1/nu) in the +-J model. We find that it holds asymptotically. This result is consistent with the low-temperature crossover scenario in which the crossover temperature, which separates the universal high-temperature region from the discrete low-temperature regime, scales as T_c(L) ~ L^(-theta_S) with theta_S \approx 0.5.

cond-mat.dis-nn↗

arXiv2011

Fluid-fluid demixing curves for colloid-polymer mixtures in a random colloidal matrix

We study fluid-fluid phase separation in a colloid-polymer mixture adsorbed in a colloidal porous matrix close to the θ-point. For this purpose we consider the Asakura-Oosawa model in the presence of a quenched matrix of colloidal hard spheres. We study the dependence of the demixing curve on the parameters that characterize the quenched matrix, fixing the polymer-to-colloid size ratio to 0.8. We find that, to a large extent, demixing curves depend only on a single parameter f, which represents the volume fraction which is unavailable to the colloids. We perform Monte Carlo simulations for volume fractions f equal to 40% and 70%, finding that the binodal curves in the polymer and colloid packing-fraction plane have a small dependence on disorder. The critical point instead changes significantly: for instance, the colloid packing fraction at criticality increases with increasing f. Finally, we observe for some values of the parameters capillary condensation of the colloids: a bulk colloid-poor phase is in chemical equilibrium with a colloid-rich phase in the matrix.

cond-mat.soft↗

arXiv2011

Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses

We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice +-J (Edwards-Anderson) Ising model with bond distribution $P(J) = p δ(J - 1) + (1-p) δ(J + 1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly reentrant. As a consequence, for an interval of the disorder parameter p, around p=0.77, the system presents a low-temperature glassy phase, an intermediate ferromagnetic phase, and a high-temperature paramagnetic phase. Along the ferromagnetic-glassy transition line magnetic correlations show a universal critical behavior with critical exponents nu=0.96(2) and eta=-0.39(2). The hyperscaling relation beta/nu = (1 + eta)/2 is satisfied at the transitions, so that beta/nu = 0.305(10). This magnetic critical behavior represents a new universality class for ferromagnetic transitions in Ising-like disordered systems. Overlap correlations are apparently not critical and show a smooth behavior across the transition.

cond-mat.dis-nn↗

arXiv2010

Geometrical Properties of Two-Dimensional Interacting Self-Avoiding Walks at the Theta-Point

We perform a Monte Carlo simulation of two-dimensional N-step interacting self-avoiding walks at the theta point, with lengths up to N=3200. We compute the critical exponents, verifying the Coulomb-gas predictions, the theta-point temperature T_theta = 1.4986(11), and several invariant size ratios. Then, we focus on the geometrical features of the walks, computing the instantaneous shape ratios, the average asphericity, and the end-to-end distribution function. For the latter quantity, we verify in detail the theoretical predictions for its small- and large-distance behavior.

cond-mat.soft↗

arXiv2010

Universality of the glassy transitions in the two-dimensional +- J Ising model

We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, is universal, i.e., independent of p. Moreover, we show that glassy and magnetic modes are not coupled at the multicritical zero-temperature point where the paramagnetic-ferromagnetic transition line and the T=0 glassy transition line meet. On the theoretical side we discuss the validity of finite-size scaling in glassy systems with a zero-temperature transition and a discrete Hamiltonian spectrum. Because of a freezing phenomenon which occurs in a finite volume at sufficiently low temperatures, the standard finite-size scaling limit in terms of $TL^{1/ν}$ does not exist: the renormalization-group invariant quantity $ξ/L$ should be used instead as basic variable.

cond-mat.dis-nn↗

arXiv2010

Magnetic and glassy transitions in the square-lattice XY model with random phase shifts

We investigate the magnetic and glassy transitions of the square-lattice XY model in the presence of random phase shifts. We consider two different random-shift distributions: the Gaussian distribution and a slightly different distribution (cosine distribution) which allows the exact determination of the Nishimori line where magnetic and overlap correlation functions are equal. We perform Monte Carlo simulations for several values of the temperature and of the variance of the disorder distribution, in the paramagnetic phase close to the magnetic and glassy transition lines. We find that, along the transition line separating the paramagnetic and the quasi-long-range order phases, magnetic correlation functions show a universal Kosterlitz-Thouless behavior as in the pure XY model, while overlap correlations show a disorder-dependent critical behavior. This behavior is observed up to a multicritical point which, in the cosine model, lies on the Nishimori line. Finally, for large values of the disorder variance, we observe a universal zero-temperature glassy critical transition, which is in the same universality class as that occurring in the gauge-glass model.

cond-mat.stat-mech↗

arXiv2009

Quasi-long-range order in the 2D XY model with random phase shifts

We study the square-lattice XY model in the presence of random phase shifts. We consider two different disorder distributions with zero average shift and investigate the low-temperature quasi-long-range order phase which occurs for sufficiently low disorder. By means of Monte Carlo simulations we determine several universal quantities which are then compared with the analytic predictions of the random spin-wave theory. We observe a very good agreement which indicates that the universal long-distance behavior in the whole low-disorder low-temperature phase is fully described by the random spin-wave theory.

cond-mat.dis-nn↗

arXiv2008

Critical and multicritical behavior of the +- J Ising model in two and three dimensions

We report our Monte Carlo results on the critical and multicritical behavior of the +- J Ising model [with a random-exchange probability P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p=1 to a multicritical (Nishimori) point. By a finite-size scaling analysis, we provide strong numerical evidence that in three dimensions the critical behavior along this line belongs to the same universality class as that of the critical transition in the randomly dilute Ising model. In two dimensions we confirm that the critical behavior is controlled by the pure Ising fixed point and that disorder is marginally irrelevant, giving rise to universal logarithmic corrections. In both two and three dimensions, we also determine the location of the multicritical Nishimori point, as well as the renormalization-group dimensions of the operators that control the renormalization-group flow close to it.

cond-mat.dis-nn↗

arXiv2008

The critical behavior of three-dimensional Ising spin glass models

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the +- J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to L=28 and L=20, respectively), and the bond-diluted bimodal model for bond-occupation probability p_b = 0.45 (up to L=16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent ωrelated to the leading irrelevant operator: ω=1.0(1). Shorter Monte Carlo simulations of the bond-diluted bimodal models at p_b=0.7 and p_b=0.35 (up to L=10) and of the Ising spin-glass model with Gaussian bond distribution (up to L=8) also support the existence of a unique Ising spin-glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents νand η: we obtain ν=2.45(15) and η=-0.375(10).

cond-mat.dis-nn↗

arXiv2008

Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice

We investigate the critical behavior of the random-bond +- J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the disorder parameter (p=1 corresponds to the pure Ising model). We perform a finite-size scaling analysis of high-statistics Monte Carlo simulations along the Nishimori line defined by $2p-1={\rm Tanh}(1/T)$, along which the multicritical point lies. The multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and the renormalization-group dimensions of the operators that control the multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to the thermal exponent ν= 1/y_2=4.00(3) and to the crossover exponent ϕ= y_1/y_2=2.62(6).

cond-mat.dis-nn↗

arXiv2008

Static and dynamic structure factors in three-dimensional randomly diluted Ising models

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.

cond-mat.dis-nn↗

arXiv2008

Third virial coefficient for 4-arm and 6-arm star polymers

We discuss the computation of the third virial coefficient in polymer systems, focusing on an additional contribution absent in the case of monoatomic fluids. We determine the interpenetration ratio and several quantities that involve the third virial coefficient for star polymers with 4 and 6 arms in the good-solvent regime, in the limit of a large degree of polymerization.

cond-mat.soft↗

arXiv2008

Nodal quasiparticles and the onset of spin density wave order in the cuprates

We present a theory for the onset of spin density wave order in the superconducting ground state of the cuprates. We compute the scaling dimensions of allowed perturbations of a `relativistic' fixed point with O(4)xO(3) symmetry, including those associated with the fermionic nodal Bogoliubov quasiparticles. Analyses of up to six loops show that all perturbations with square lattice symmetry are likely irrelevant. We demonstrate that the fermion spectral functions are primarily damped by the coupling to fluctuations of a composite field with Ising nematic order. We also discuss the influence of quenched disorder.

cond-mat.str-el↗

arXiv2007

High-order perturbative expansions of multi-parameter Phi^4 quantum field theories

We present high-order pertubative expansions of multi-parameter Phi^4 quantum field theories with an N-component fundamental field, containing up to 4th-order polynomials of the field. Multi-parameter Phi^4 theories generalize the simplest O(N)-symmetric Phi^4 theories, and describe more complicated symmetry breaking patterns. These notes collect several high-order perturbative series of physically interesting multi-parameter Phi^4 theories, to five or six loops. We consider the O(M)XO(N)-symmetric Phi^4 model, the so-called MN model, and a spin-density-wave Phi^4 model containing five quartic terms.

hep-th↗

arXiv2007

The uniformly frustrated two-dimensional XY model in the limit of weak frustration

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array, in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behaviour of the XY model for T <= T_{KT}, where T_{KT} is the Kosterlitz-Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behaviour of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.

cond-mat.stat-mech↗

arXiv2007

Two-parameter model predictions and theta-point crossover for linear-polymer solutions

We consider the first few virial coefficients of the osmotic pressure, the radius of gyration, the hydrodynamic radius, and the end-to-end distance for a monodisperse polymer solution. We determine the corresponding two-parameter model functions which parametrize the crossover between the good-solvent and the ideal-chain behavior. These results allow us to predict the osmotic pressure and the polymer size in the dilute regime in a large temperature region above the theta-point.

cond-mat.soft↗