arXiv subjects

Ettore Vicari

Publications and source records attributed to Ettore Vicari.

At least 181 records · Page 10Linked to original sources

arXiv2006

The critical exponents of the superfluid transition in He4

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class, which apply to the superfluid transition in He4 along the lambda-line of its phase diagram. We obtain the estimates alpha=-0.0151(3), nu=0.6717(1), eta=0.0381(2), gamma=1.3178(2), beta=0.3486(1), and delta=4.780(1). Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size L=128 and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent alpha disagrees with the most recent experimental estimate alpha=-0.0127(3) at the superfluid transition of He4 in microgravity environment.

cond-mat.stat-mech↗

arXiv2006

Corrections to scaling in multicomponent polymer solutions

We calculate the correction-to-scaling exponent $ω_T$ that characterizes the approach to the scaling limit in multicomponent polymer solutions. A direct Monte Carlo determination of $ω_T$ in a system of interacting self-avoiding walks gives $ω_T = 0.415(20)$. A field-theory analysis based on five- and six-loop perturbative series leads to $ω_T = 0.41(4)$. We also verify the renormalization-group predictions for the scaling behavior close to the ideal-mixing point.

cond-mat.soft↗

arXiv2006

Spin-density-wave order in cuprates

We study the nature of the two-dimensional quantum critical point separating two phases with and without long-range spin-density-wave order, which has been recently observed in cuprate superconductors. We consider the Landau-Ginzburg-Wilson Hamiltonian associated with the spin-density critical modes, perform a mean-field analysis of the phase diagram, and study the corresponding renormalization-group flow in two different perturbative schemes at five and six loops, respectively. The analysis supports the existence of a stable fixed point in the full theory whose basin of attraction includes systems with collinear spin-density-wave order, as observed in experiments. The stable fixed point is characterized by an enlarged O(4)xO(3) symmetry. The continuous transition observed in experiments is expected to belong to this universality class. The corresponding critical exponents are nu = 0.9(2) and eta = 0.15(10).

cond-mat.stat-mech↗

arXiv2005

Multicritical behavior in the fully frustrated XY model and related systems

We study the phase diagram and critical behavior of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on square lattices L x L, up to L=O(10^3). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range order. The FFXY model and the other models in a rather large parameter region show a crossover behavior at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behavior is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero-temperature transition. A possible candidate is the O(4) point that controls the low-temperature behavior of the 4-vector model.

cond-mat.stat-mech↗

arXiv2005

Critical behavior of two-dimensional fully frustrated XY systems

We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices $L\times L$, $L\lesssim 10^3$. We show that the low-temperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent $ν_{\rm eff} \approx 0.8$. This explains the result $ν\approx 0.8$ of many previous studies using smaller lattices.

cond-mat.stat-mech↗

arXiv2005

Finite-temperature chiral transition in QCD with quarks in the fundamental and adjoint representation

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the fundamental and adjoint representation. Universality and renormalization-group (RG) arguments show that the possibility of having a continuous transition is related to the existence of a stable fixed point (FP) in the RG flow of a 3D Landau-Ginzburg-Wilson Phi^4 theory with the same chiral symmetry-breaking pattern. The RG flow of these theories is studied by field-theoretical approaches, computing and analyzing high-order perturbative series, up to six loops. According to this RG analysis, the transition in QCD can be continuous only for N_f=2. In this case it belongs to the 3D O(4) universality class. We also find a stable FP corresponding to a 3D universality class with symmetry breaking U(2)_L x U(2)_R -> U(2)_V, which implies that the transition can be continuous also if the axial-anomaly effects are suppressed at Tc. In the case of quarks in the adjoint representation, we can have a continuous transition for N_f=1,2. For N_f=1 it belongs to the O(3) universality class. For N_f=2 it belongs to a new 3D universality class characterized by the symmetry breaking SU(4)->SO(4).

hep-lat↗

arXiv2005

Transitions and crossover phenomena in fully frustrated XY systems

We study the two-dimensional fully frustrated XY (FFXY) model and two related models, a discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model and a coupled Ising-XY model, by means of Monte Carlo simulations on square lattices L x L, L=O(10^3). We show that their phase diagram is characterized by two very close chiral and spin transitions, at T_ch > T_sp respectively, of the Ising and Kosterlitz-Thouless type. At T_ch the Ising regime sets in only after a preasymptotic regime, which appears universal to some extent. The approach is nonmonotonic for most observables, with a wide region controlled by an effective exponent nu_eff=0.8.

cond-mat.stat-mech↗

arXiv2005

Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors

We study the nature of the multicritical point in the three-dimensional O(3)+O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the competition of two order parameters that are O(3) and O(2) symmetric, respectively. This study is relevant for the SO(5) theory of high-Tc superconductors, which predicts the existence of a multicritical point in the temperature-doping phase diagram, where the antiferromagnetic and superconducting transition lines meet. We investigate whether the O(3)+O(2) symmetry gets effectively enlarged to O(5) approaching the multicritical point. For this purpose, we study the stability of the O(5) fixed point. By means of a Monte Carlo simulation, we show that the O(5) fixed point is unstable with respect to the spin-4 quartic perturbation with the crossover exponent $ϕ_{4,4}=0.180(15)$, in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop $ε$-expansion estimate $ϕ_{4,4}=1/26$, which has often been used in the literature to discuss the multicritical behavior within the SO(5) theory. Therefore, no symmetry enlargement is generically expected at the multicritical transition. We also perform a five-loop field-theoretical analysis of the renormalization-group flow. It shows that bicritical systems are not in the attraction domain of the stable decoupled fixed point. Thus, in these systems--high-Tc cuprates should belong to this class--the multicritical point corresponds to a first-order transition.

cond-mat.supr-con↗

arXiv2005

Quantum Field Theories and Critical Phenomena on Defects

We construct and investigate quantum fields induced on a d-dimensional dissipationless defect by bulk fields propagating in a (d+1)-dimensional space. All interactions are localized on the defect. We derive a unitary non-canonical quantum field theory on the defect, which is analyzed both in the continuum and on the lattice. The universal critical behavior of the underlying system is determined. It turns out that the O(N)-symmetric phi^4 theory, induced on the defect by massless bulk fields, belongs to the universality class of particular d-dimensional spin models with long-range interactions. On the other hand, in the presence of bulk mass the critical behavior crossovers to the one of d-dimensional spin models with short-range interactions.

hep-th↗

arXiv2004

The finite-temperature chiral transition in QCD with adjoint fermions

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.

hep-th↗

arXiv2004

Interacting N-vector order parameters with O(N) symmetry

We consider the critical behavior of the most general system of two N-vector order parameters that is O(N) invariant. We show that it may a have a multicritical transition with enlarged symmetry controlled by the chiral O(2)xO(N) fixed point. For N=2, 3, 4, if the system is also invariant under the exchange of the two order parameters and under independent parity transformations, one may observe a critical transition controlled by a fixed point belonging to the mn model. Also in this case there is a symmetry enlargement at the transition, the symmetry being [SO(N)+SO(N)]xC_2, where C_2 is the symmetry group of the square.

hep-th↗

arXiv2004

Topological susceptibility of SU(N) gauge theories at finite temperature

We investigate the large-N behavior of the topological susceptibility in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at Tc. For this purpose, we consider the lattice formulation of the SU(N) gauge theories and perform Monte Carlo simulations for N=4,6. The results indicate that the topological susceptibility has a nonvanishing large-N limit for T Tc.

hep-th↗

arXiv2004

Critical behavior of O(2)xO(N) symmetric models

We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking pattern O(2)xO(N) -> O(2)xO(N-2). Physical realizations of these systems are, for example, frustrated spin models with noncollinear order. Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, we consider the massless critical theory and the minimal-subtraction scheme without epsilon expansion. The three-dimensional analysis of the corresponding five-loop expansions shows the existence of a stable fixed point for N=2 and N=3, confirming recent field-theoretical results based on a six-loop expansion in the alternative zero-momentum renormalization scheme defined in the massive disordered phase. In addition, we report numerical Monte Carlo simulations of a class of three-dimensional O(2)xO(2)-symmetric lattice models. The results provide further support to the existence of the O(2)xO(2) universality class predicted by the field-theoretical analyses.

cond-mat.stat-mech↗

arXiv2004

The scaling equation of state of the three-dimensional O(N) universality class: N >= 4

We determine the critical equation of state of the three-dimensional O(N) universality class, for N=4, 5, 6, 32, 64. The N=4 is relevant for the chiral phase transition in QCD with two flavors, the N=5 model is relevant for the SO(5) theory of high-T_c superconductivity, while the N=6 model is relevant for the chiral phase transition in two-color QCD with two flavors. We first consider the small-field expansion of the effective potential (Helmholtz free energy). Then, we apply a systematic approximation scheme based on polynomial parametric representations that are valid in the whole critical regime, satisfy the correct analytic properties (Griffiths' analyticity), take into account the Goldstone singularities at the coexistence curve, and match the small-field expansion of the effective potential. From the approximate representations of the equation of state, we obtain estimates of universal amplitude ratios. We also compare our approximate solutions with those obtained in the large-N expansion, up to order 1/N, finding good agreement for N \gtrsim 32.

hep-lat↗

arXiv2004

Multicritical behavior in frustrated spin systems with noncollinear order

We investigate the phase diagram and, in particular, the nature of the the multicritical point in three-dimensional frustrated $N$-component spin models with noncollinear order in the presence of an external field, for instance easy-axis stacked triangular antiferromagnets in the presence of a magnetic field along the easy axis. For this purpose we study the renormalization-group flow in a Landau-Ginzburg-Wilson ϕ^4 theory with symmetry O(2)x[Z_2 +O(N-1)] that is expected to describe the multicritical behavior. We compute its MS βfunctions to five loops. For N\ge 4, their analysis does not support the hypothesis of an effective enlargement of the symmetry at the multicritical point, from O(2) x [Z_2+O(N-1)] to O(2)xO(N). For the physically interesting case N=3, the analysis does not allow us to exclude the corresponding symmetry enlargement controlled by the O(2)xO(3) fixed point. Moreover, it does not provide evidence for any other stable fixed point. Thus, on the basis of our field-theoretical results, the transition at the multicritical point is expected to be either continuous and controlled by the O(2)xO(3) fixed point or to be of first order.

cond-mat.stat-mech↗

arXiv2004

Critical slowing down of topological modes

We investigate the critical slowing down of the topological modes using local updating algorithms in lattice 2-d CP^(N-1) models. We show that the topological modes experience a critical slowing down that is much more severe than the one of the quasi-Gaussian modes relevant to the magnetic susceptibility, which is characterized by $τ_{\rm mag} \sim ξ^z$ with $z\approx 2$. We argue that this may be a general feature of Monte Carlo simulations of lattice theories with non-trivial topological properties, such as QCD, as also suggested by recent Monte Carlo simulations of 4-d SU(N) lattice gauge theories.

hep-lat↗

arXiv2004

Crossover behavior in three-dimensional dilute spin systems

We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the Gaussian-to-random and the pure-Ising-to-random crossover, determining the corresponding crossover functions for the magnetic susceptibility and the correlation length. Moreover, for the physically interesting cases of dilute Ising, XY, and Heisenberg systems, we estimate several universal ratios of scaling-correction amplitudes entering the high-temperature Wegner expansion of the magnetic susceptibility, of the correlation length, and of the zero-momentum quartic couplings.

cond-mat.stat-mech↗

arXiv2003

The normal-to-planar superfluid transition in Helium 3

We study the nature of the Helium-3 superfluid transition from the normal to the planar phase, which is expected to be stabilized by the dipolar interactions. We determine the RG flow of the corresponding Landau-Ginzburg-Wilson theory by exploiting two fixed-dimension perturbative schemes: the massive zero-momentum scheme and the minimal-subtraction scheme without $ε$ expansion. The analysis of the corresponding six-loop and five-loop series shows the presence of a stable fixed point in the relevant coupling region. Therefore, we predict the transition to be continuous. We also compute critical exponents. The specific-heat exponent $α$ is estimated as $α= 0.20(15)$, while the magnetic susceptibility and magnetization exponents $γ_H$ and $β_H$ for Helium 3 are $γ_H = -0.34(5)$, $β_H = 1.07(9)$.

cond-mat.stat-mech↗