Searcharxiv⌕ Search

arXiv subjects

Andrea Pelissetto

Publications and source records attributed to Andrea Pelissetto.

At least 163 records · Page 9Linked to original sources
arXiv2003

The critical behavior of magnetic systems described by Landau-Ginzburg-Wilson field theories

We discuss the critical behavior of several three-dimensional magnetic systems, such as pure and randomly dilute (anti)ferromagnets and stacked triangular antiferromagnets. We also discuss the nature of the multicritical points that arise in the presence of two distinct O(n)-symmetric order parameters and, in particular, the nature of the multicritical point in the phase diagram of high-T_c superconductors that has been predicted by the SO(5) theory. For each system, we consider the corresponding Landau-Ginzburg-Wilson field theory and review the field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the epsilon and of the fixed-dimension d=3 expansions.

cond-mat.stat-mech↗
arXiv2003

The 3-D O(4) universality class and the phase transition in two-flavor QCD

We determine the critical equation of state of the three-dimensional O(4) universality class. 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 several universal amplitude ratios. The three-dimensional O(4) universality class is expected to describe the finite-temperature chiral transition of quantum chromodynamics with two light flavors. Within this picture, the O(4) critical equation of state relates the reduced temperature, the quark masses, and the condensates around T_c in the limit of vanishing quark masses.

hep-ph↗
arXiv2003

Comment on ``Dynamic behavior of anisotropic non-equilibrium driving lattice gases''

In a recent Letter Albano and Saracco study the dynamic critical behavior of some anisotropic driven lattice gases by Monte Carlo (MC) simulations. In this Comment we point out that the Ansätze they use to relate the measured scaling exponents with the critical exponents analytically computed within different field-theoretical approaches do not take properly into account the strongly anisotropic nature of the phase transition, by implicitly assuming $z = z_{\bot} = z_{\parallel}$. As a consequence, at variance with the claims by the authors, their MC data are not conclusive to determine which one of the field theories proposed in the literature correctly describes the universal properties of the phase transition in these lattice gases.

cond-mat↗
arXiv2003

Shape dependence of the finite-size scaling limit in a strongly anisotropic $O(\infty)$ model

We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the related exponents may only be effective ones, differing from the correct critical exponents of the model. We discuss the implications of our results for numerical finite-size scaling studies of strongly anisotropic systems.

cond-mat.stat-mech↗
arXiv2003

Third-harmonic exponent in three-dimensional N-vector models

We compute the crossover exponent associated with the spin-3 operator in three-dimensional O(N) models. A six-loop field-theoretical calculation in the fixed-dimension approach gives $ϕ_3 = 0.601(10)$ for the experimentally relevant case N=2 (XY model). The corresponding exponent $β_3 = 1.413(10)$ is compared with the experimental estimates obtained in materials undergoing a normal-incommensurate structural transition and in liquid crystals at the smectic-A--hexatic-B phase transition, finding good agreement.

cond-mat.stat-mech↗
arXiv2003

Randomly dilute spin models with cubic symmetry

We study the combined effect of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. For this purpose, we consider the field-theoretical approach based on the Ginzburg-Landau-Wilson $ϕ^4$ Hamiltonian with cubic-symmetric quartic interactions and quenched randomness coupled to the local energy density. We compute the renormalization-group functions to six loops in the fixed-dimension (d=3) perturbative scheme. The analysis of such high-order series provides an accurate description of the renormalization-group flow. The results are also used to determine the critical behavior of three-dimensional antiferromagnetic three- and four-state Potts models in the presence of quenched impurities.

cond-mat.stat-mech↗
arXiv2002

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $ϕ^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $ε$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.

hep-th↗
arXiv2002

Transverse Fluctuations in the Driven Lattice Gas

We define a transverse correlation length suitable to discuss the finite-size-scaling behavior of an out-of-equilibrium lattice gas, whose correlation functions decay algebraically with the distance. By numerical simulations we verify that this definition has a good infinite-volume limit independent of the lattice geometry. We study the transverse fluctuations as they can select the correct field-theoretical description. By means of a careful finite-size scaling analysis, without tunable parameters, we show that they are Gaussian, in agreement with the predictions of the model proposed by Janssen, Schmittmann, Leung, and Cardy.

cond-mat.stat-mech↗
arXiv2002

Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories

We study the multicritical behavior arising from the competition of two distinct types of ordering characterized by O(n) symmetries. For this purpose, we consider the renormalization-group flow for the most general $O(n_1)\oplus O(n_2)$-symmetric Landau-Ginzburg-Wilson Hamiltonian involving two fields $ϕ_1$ and $ϕ_2$ with $n_1$ and $n_2$ components respectively. In particular, we determine in which cases, approaching the multicritical point, one may observe the asymptotic enlargement of the symmetry to O(N) with N=n_1+n_2. By performing a five-loop $ε$-expansion computation we determine the fixed points and their stability. It turns out that for N=n_1+n_2\ge 3 the O(N)-symmetric fixed point is unstable. For N=3, the multicritical behavior is described by the biconal fixed point with critical exponents that are very close to the Heisenberg ones. For N\ge 4 and any n_1,n_2 the critical behavior is controlled by the tetracritical decoupled fixed point. We discuss the relevance of these results for some physically interesting systems, in particular for anisotropic antiferromagnets in the presence of a magnetic field and for high-T_c superconductors. Concerning the SO(5) theory of superconductivity, we show that the bicritical O(5) fixed point is unstable with a significant crossover exponent, $ϕ_{4,4}\approx 0.15$; this implies that the O(5) symmetry is not effectively realized at the point where the antiferromagnetic and superconducting transition lines meet. The multicritical behavior is either governed by the tetracritical decoupled fixed point or is of first-order type if the system is outside its attraction domain.

cond-mat.stat-mech↗
arXiv2002

Critical Phenomena and Renormalization-Group Theory

We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of self-avoiding walks. For each of them, we review the estimates of the critical exponents, of the equation of state, of several amplitude ratios, and of the two-point function of the order parameter. We report results in three and two dimensions. We discuss the crossover phenomena that are observed in this class of systems. In particular, we review the field-theoretical and numerical studies of systems with medium-range interactions. Moreover, we consider several examples of magnetic and structural phase transitions, which are described by more complex Landau-Ginzburg-Wilson Hamiltonians, such as $N$-component systems with cubic anisotropy, O($N$)-symmetric systems in the presence of quenched disorder, frustrated spin systems with noncollinear or canted order, and finally, a class of systems described by the tetragonal Landau-Ginzburg-Wilson Hamiltonian with three quartic couplings. The results for the tetragonal Hamiltonian are original, in particular we present the six-loop perturbative series for the $β$-functions. Finally, we consider a Hamiltonian with symmetry $O(n_1)\oplus O(n_2)$ that is relevant for the description of multicritical phenomena.

cond-mat.stat-mech↗
arXiv2002

Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)]

We show that, in the most general $N$-component theory with symmetry O(n_1)+O(n_2), N=n_1+n_2\geq 3, the O(N)-symmetric fixed point has (at least) three unstable directions: the temperature, the quadratic anisotropy, and the spin-4 quartic perturbation. This implies that in the SO(5) theory of high-$T_c$ superconductivity an additional tuning is required to obtain an enlarged SO(5) symmetry. This is in contrast with the recent numerical results reported by Hu, Phys. Rev. Lett. 87, 057004 (2001). \

cond-mat.supr-con↗
arXiv2002

Two-Dimensional Heisenberg Model with Nonlinear Interactions

We investigate a two-dimensional classical $N$-vector model with a nonlinear interaction $(1 + \bsigma_i\cdot \bsigma_j)^p$ in the large-N limit. As observed for N=3 by Blöte {\em et al.} [Phys. Rev. Lett. {\bf 88}, 047203 (2002)], we find a first-order transition for $p>p_c$ and no finite-temperature phase transitions for $p < p_c$. For $p>p_c$, both phases have short-range order, the correlation length showing a finite discontinuity at the transition. For $p=p_c$, there is a peculiar transition, where the spin-spin correlation length is finite while the energy-energy correlation length diverges.

cond-mat.stat-mech↗
arXiv2002

Critical structure factor in Ising systems

We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L^3 with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernicke expression of Puglielli and Ford.

cond-mat.stat-mech↗
arXiv2002

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $γ=1.2373(2)$, $ν=0.63012(16)$, $α=0.1096(5)$, $η=0.03639(15)$, $β=0.32653(10)$, $δ=4.7893(8)$. Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $Δ=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.

cond-mat.stat-mech↗
arXiv2001

Structure factor of dilute ring polymers

We consider ring polymers in good solvents in the dilute limit. We determine the structure factor and the monomer-monomer distribution function. We compute accurately the asymptotic behavior of these functions for small and large momenta and distances by using field-theoretical methods. Phenomenological expressions with the correct asymptotic behaviors are also given.

cond-mat.stat-mech↗
arXiv2001

Critical structure factors of bilinear fields in O(N)-vector models

We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum behavior of the corresponding scaling functions, and give general interpolation formulae based on a dispersive approach. Moreover, we determine the crossover exponent $ϕ_T$ associated with the traceless tensorial quadratic field, by computing and analyzing its six-loop perturbative expansion in fixed dimension. We find: $ϕ_T=1.184(12)$, $ϕ_T=1.271(21)$, and $ϕ_T=1.40(4)$ for $N=2,3,5$ respectively.

cond-mat.stat-mech↗
arXiv2001

Discrete non-Abelian groups and asymptotically free models

We consider a two-dimensional $σ$-model with discrete icosahedral/dodecahedral symmetry. Using the perturbative renormalization group, we argue that this model has a different continuum limit with respect to the O(3) $σ$ model. Such an argument is confirmed by a high-precision numerical simulation.

hep-lat↗