arXiv subjects

Andrea Pelissetto

Publications and source records attributed to Andrea Pelissetto.

At least 91 records · Page 5Linked to original sources

arXiv2015

Relevance of the axial anomaly at the finite-temperature chiral transition in QCD

We investigate the nature of the finite-temperature chiral transition in QCD with two light flavors, in the case of an effective suppression of the the U(1)_A symmetry breaking induced by the axial anomaly, which implies the symmetry breaking U(2)_L X U(2)_R -> U(2)_V, instead of SU(2)_L X SU(2)_R -> SU(2)_V. For this purpose, we perform a high-order field-theoretical perturbative study of the renormalization-group (RG) flow of the corresponding three-dimensional multiparameter Landau-Ginzburg-Wilson Phi4 theory with the same symmetry-breaking pattern. We confirm the existence of a stable fixed point (FP), and determine its attraction domain in the space of the bare quartic parameters. Therefore, the chiral QCD transition might be continuous also if the U(1)_A symmetry is effectively restored at Tc. However, the corresponding universality class differs from the O(4) vector universality class which would describe a continuous transition in the presence of a substantial U(1)_A symmetry breaking at Tc. We estimate the critical exponents of the U(2)_L X U(2)_R -> U(2)_V universality class by computing and analyzing their high-order perturbative expansions. These results are important to discriminate among the different scenarios for the scaling behavior of QCD with two light flavors close to the chiral transition.

hep-lat↗

arXiv2015

Bose-Einstein condensation and critical behavior of two-component bosonic gases

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson Phi4 theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange Z_2,e symmetry, coupled by effective density-density interactions, the global symmetry is Z_2e X U(1) X U(1). At the BEC transition it may break into Z_2,e X Z_2 X Z_2 when both components condense simultaneously, or to U(1) X Z_2 when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly-decaying scaling corrections arising from the on-site inter-species interaction.

cond-mat.stat-mech↗

arXiv2015

Three-dimensional antiferromagnetic CP(N-1) models

We investigate the critical behavior of three-dimensional antiferromagnetic CP(N-1) [ACP(N-1)] models in cubic lattices, which are characterized by a global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-Ginzburg-Wilson (LGW) model. For N=3 this mapping allows us to conclude that the three-component ACP(2) model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP(2) and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N>3. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.

cond-mat.stat-mech↗

arXiv2015

Integral-equation analysis of single-site coarse-grained models for polymer-colloid mixtures

We discuss the reliability of integral-equation methods based on several commonly used closure relations in determining the phase diagram of coarse-grained models of soft-matter systems characterized by mutually interacting soft and hard-core particles. Specifically, we consider a set of potentials appropriate to describe a system of hard-sphere colloids and linear homopolymers in good solvent, and investigate the behavior when the soft particles are smaller than the colloids, which is the regime of validity of the coarse-grained models. Using computer-simulation results as a benchmark, we find that the hypernetted-chain approximation provides accurate estimates of thermodynamics and structure in the colloid-gas phase in which the density of colloids is small. On the other hand, all closures considered appear to be unable to describe the behavior of the mixture in the colloid-liquid phase, as they cease to converge at polymer densities significantly smaller than those at the binodal. As a consequence, integral equations appear to be unable to predict a quantitatively correct phase diagram.

cond-mat.soft↗

arXiv2015

Quantum transitions driven by one-bond defects in quantum Ising rings

We investigate quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models. We consider quantum Ising rings in the presence of a bond defect. In the ordered phase, the system undergoes a quantum transition driven by the bond defect between a magnet phase, in which the gap decreases exponentially with increasing size, and a kink phase, in which the gap decreases instead with a power of the size. Close to the transition, the system shows a universal scaling behavior, which we characterize by computing, either analytically or numerically, scaling functions for the gap, the susceptibility, and the two-point correlation function. We discuss the implications of these results for the nonequilibrium dynamics in the presence of a slowly-varying parallel magnetic field h, when going across the first-order quantum transition at h=0.

cond-mat.stat-mech↗

arXiv2015

Coarse-graining polymer solutions: a critical appraisal of single- and multi-site models

We critically discuss and review the general ideas behind single- and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems presenting, as a test case, results for mixtures of colloids and polymers. Specifically, we found the CG model with zero-density potentials to be unable to predict fluid-fluid demixing in a reasonable range of densities for mixtures of colloids and polymers of equal size. For larger colloids, the polymer volume fractions at which phase separation occurs are largely overestimated. CG models with density-dependent potentials are somewhat less accurate than models with zero-density potentials in reproducing the thermodynamics of the system and, although they presents a phase separation, they significantly underestimate the polymer volume fractions along the binodal. Finally, we discuss a general multi-site strategy, which is thermodynamically consistent and fully transferable with the number of sites, and that allows us to overcome most of the limitations discussed for single-site models.

cond-mat.soft↗

arXiv2014

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQT), such as those arising from the presence of a space-dependent external field, which smooths out the typical discontinuities of the low-energy properties. We argue that scaling phenomena develop at the transition region where the external field takes the value corresponding to the FOQT of the homogenous system. We present numerical evidence of such scaling phenomena at the FOQTs of quantum Ising chains, driven by a parallel magnetic field when the system is in the ferromagnetic phase, and at the FOQT of the q-state Potts chain for q>4, driven by an even temperature-like parameter giving rise to a discontinuity of the ground-state energy density.

cond-mat.stat-mech↗

arXiv2014

Finite-size scaling at the first-order quantum transitions of quantum Potts chains

We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q>4, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. The low-energy properties around the transition show finite-size scaling, described by general scaling ansatzes with respect to appropriate scaling variables. The size dependence of the scaling variables presents a particular sensitiveness to boundary conditions, which may be considered as a peculiar feature of first-order quantum transitions.

cond-mat.stat-mech↗

arXiv2014

Accurate coarse-grained models for mixtures of colloids and linear polymers under good-solvent conditions

A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach groups of monomers are mapped onto a single pseudoatom (a blob) and the effective blob-blob interactions are obtained by requiring the model to reproduce some large-scale structural properties in the zero-density limit. We show that an accurate parametrization of the polymer-colloid interactions is obtained by simply introducing pair potentials between blobs and colloids. For the coarse-grained model in which polymers are modelled as four-blob chains (tetramers), the pair potentials are determined by means of the iterative Boltzmann inversion scheme, taking full-monomer pair correlation functions at zero-density as targets. For a larger number $n$ of blobs, pair potentials are determined by using a simple transferability assumption based on the polymer self-similarity. We validate the model by comparing its predictions with full-monomer results for the interfacial properties of polymer solutions in the presence of a single colloid and for thermodynamic and structural properties in the homogeneous phase at finite polymer and colloid density. The tetramer model is quite accurate for $q\lesssim 1$ ($q=\hat{R}_g/R_c$, where $\hat{R}_g$ is the zero-density polymer radius of gyration and $R_c$ is the colloid radius) and reasonably good also for $q=2$. For $q=2$ an accurate coarse-grained description is obtained by using the $n=10$ blob model. We also compare our results with those obtained by using single-blob models with state-dependent potentials.

cond-mat.soft↗

arXiv2014

Finite-size scaling at first-order quantum transitions

We study finite-size effects at first-order quantum transitions (FOQTs). We show that the low-energy properties show a finite-size scaling (FSS) behavior, the relevant scaling variable being the ratio of the energy associated with the perturbation driving the transition and the finite-size energy gap at the FOQT point. The size dependence of the scaling variable is therefore essentially determined by the size dependence of the gap at the transition, which in turn depends on the boundary conditions. Our results have broad validity and, in particular, apply to any FOQT characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. In this case, a phenomenological two-level theory provides exact expressions for the scaling functions. Numerical results for the quantum Ising chain in transverse and parallel magnetic fields support the FSS ansatzes.

cond-mat.stat-mech↗

arXiv2014

Depletion effects in colloid-polymer solutions

The surface tension, the adsorption, and the depletion thickness of polymers close to a single nonadsorbing colloidal sphere are computed by means of Monte Carlo simulations. We consider polymers under good-solvent conditions and in the thermal crossover region between good-solvent and $θ$ behavior. In the dilute regime we consider a wide range of values of $q$, from $q = 0$ (planar surface) up to $q\approx 30$-50, while in the semidilute regime, for $ρ_p/ρ_p^*\le 4$ ($ρ_p$ is the polymer concentration and $ρ_p^*$ is its value at overlap), we only consider $q = 0,0.5,1$ and 2. The results are compared with the available theoretical predictions, verifying the existing scaling arguments. Field-theoretical results, both in the dilute and in the semidilute regime, are in good agreement with the numerical estimates for polymers under good-solvent conditions.

cond-mat.soft↗

arXiv2014

Finite-size scaling at quantum transitions

We develop the finite-size scaling (FSS) theory at quantum transitions, considering generic boundary conditions, such as open and periodic boundary conditions, and also the corrections to the leading FSS behaviors. Using renormalization-group (RG) theory, we generalize Wegner's scaling Ansatz to the quantum case, classifying the different sources of scaling corrections. We identify nonanalytic corrections due to irrelevant (bulk and boundary) RG perturbations and analytic contributions due to regular backgrounds and analytic expansions of the nonlinear scaling fields. To check the general predictions, we consider the quantum XY chain in a transverse field. For this model exact or numerically accurate results can be obtained by exploiting its fermionic quadratic representation. We study the FSS of several observables, such as the free energy, the energy differences between low-energy levels, correlation functions of the order parameter, etc., confirming the general predictions in all cases. Moreover, we consider bipartite entanglement entropies, which are characterized by the presence of additional scaling corrections, as predicted by conformal field theory.

cond-mat.stat-mech↗

arXiv2013

Predicting the thermodynamics by using state-dependent interactions

We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distributions functions of the original system as accurately as possible. We consider standard expressions for pressure and chemical potential applied to this family of coarse-grained models with density-dependent interactions and show that they only provide approximations to the pressure and chemical potential of the underlying original system. These approximations are then carefully compared in two cases: we consider a generic microscopic system in the low-density regime and polymer solutions under good-solvent conditions. Moreover, we show that the state-dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.

cond-mat.stat-mech↗

arXiv2013

Consistent coarse-graining strategy for polymer solutions in the thermal crossover from Good to Theta solvent

We extend our previously developed coarse-graining strategy for linear polymers with a tunable number n of effective atoms (blobs) per chain [D'Adamo et al., J. Chem. Phys. 137, 4901 (2012)] to polymer systems in thermal crossover between the good-solvent and the Theta regimes. We consider the thermal crossover in the region in which tricritical effects can be neglected, i.e. not too close to the Theta point, for a wide range of chain volume fractions Phi=c/c* (c* is the overlap concentration), up to Phi=30. Scaling crossover functions for global properties of the solution are obtained by Monte-Carlo simulations of the Domb-Joyce model. They provide the input data to develop a minimal coarse-grained model with four blobs per chain. As in the good-solvent case, the coarse-grained model potentials are derived at zero density, thus avoiding the inconsistencies related to the use of state-dependent potentials. We find that the coarse-grained model reproduces the properties of the underlying system up to some reduced density which increases when lowering the temperature towards the Theta state. Close to the lower-temperature crossover boundary, the tetramer model is accurate at least up to Phi<10, while near the good-solvent regime reasonably accurate results are obtained up to Phi<2. The density region in which the coarse-grained model is predictive can be enlarged by developing coarse-grained models with more blobs per chain. We extend the strategy used in the good-solvent case to the crossover regime. This requires a proper treatment of the length rescalings as before, but also a proper temperature redefinition as the number of blobs is increased. The case n=10 is investigated. Comparison with full-monomer results shows that the density region in which accurate predictions can be obtained is significantly wider than that corresponding to the n=4 case.

cond-mat.soft↗

arXiv2013

Comparing different coarse-grained potentials for star polymers

We compare different coarse-grained models for star polymers. We find that phenomenological models inspired by the Daoud-Cotton model reproduce quite poorly the thermodynamics of these systems, even if the potential is assumed to be density dependent, as done in the analysis of experimental results. We also determine the minumum value fc of the functionality of the star polymer for which a fluid-solid transition occurs. By applying the Hansen-Verlet criterion we find 35 < fc < 40. This result is confirmed by an analysis based on the modified (reference) hypernetted chain method and is qualitatively consistent with previous work.

cond-mat.soft↗

arXiv2012

Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions

We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding beta-functions to a universal canonical form, valid to all perturbative orders. Then, we determine the asymptotic solutions of the RG equations in various critical regimes: the infinite-volume critical behavior in the disordered phase, the finite-size scaling limit for homogeneous systems of finite size, and the trap-size scaling limit occurring in 2D bosonic particle systems trapped by an external space-dependent potential.

cond-mat.stat-mech↗

arXiv2012

Colloids and polymers in random colloidal matrices: demixing under good-solvent conditions

We consider a simplified coarse-grained model for colloid-polymer mixtures, in which polymers are represented as monoatomic molecules interacting by means of pair potentials. We use it to study polymer-colloid segregation in the presence of a quenched matrix of colloidal hard spheres. We fix the polymer-to-colloid size ratio to 0.8 and consider matrices such that the fraction f of the volume that is not accessible to the colloids due to the matrix is equal to 40%. As in the Asakura-Oosawa-Vrij (AOV) case, we find that binodal curves in the polymer and colloid volume-fraction plane have a small dependence on disorder. As for the position of the critical point, the behavior is different from that observed in the AOV case: while the critical colloid volume fraction is essentially the same in the bulk and in the presence of the matrix, the polymer volume fraction at criticality increases as f increases. At variance with the AOV case, no capillary colloid condensation or evaporation is generically observed.

cond-mat.soft↗

arXiv2012

Consistent and transferrable coarse-grained model for semidilute polymer solutions in good solvent

We present a coarse-grained model for linear polymers with a tunable number of effective atoms (blobs) per chain interacting by intra- and inter-molecular potentials obtained at zero density. We show how this model is able to accurately reproduce the universal properties of the underlying solution of athermal linear chains at various levels of coarse-graining and in a range of chain densities which can be widened by increasing the spatial resolution of the multiblob representation, i.e., the number of blobs per chain. The present model is unique in its ability to quantitatively predict thermodynamic and large scale structural properties of polymer solutions deep in the semidilute regime with a very limited computational effort, overcoming most of the problems related to the simulations of semidilute polymer solutions in good solvent conditions.

cond-mat.soft↗