88 research outputs found
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.Comment: 9 page
Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic field
We study the phase diagram and multicritical behavior of anisotropic
Heisenberg antiferromagnets on a square lattice in the presence of a magnetic
field along the easy axis. We argue that, beside the Ising and XY critical
lines, the phase diagram presents a first-order spin-flop line starting from
T=0, as in the three-dimensional case. By using field theory we show that the
multicritical point where these transition lines meet cannot be O(3) symmetric
and occurs at finite temperature. We also predict how the critical temperature
of the transition lines varies with the magnetic field and the uniaxial
anisotropy in the limit of weak anisotropy.Comment: 21 pages, 8 fig
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 , in substantial
agreement with recent field-theoretical results. This estimate is much larger
than the one-loop -expansion estimate , 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.Comment: 18 page
High-precision estimate of g4 in the 2D Ising model
We compute the renormalized four-point coupling in the 2d Ising model using
transfer-matrix techniques. We greatly reduce the systematic uncertainties
which usually affect this type of calculations by using the exact knowledge of
several terms in the scaling function of the free energy. Our final result is
g4=14.69735(3).Comment: 17 pages, revised version with minor changes, accepted for
publication in Journal of Physics
The critical behavior of 3D Ising glass models: universality and scaling corrections
We perform high-statistics Monte Carlo simulations of three three-dimensional
Ising spin-glass models: the +-J Ising model for two values of the disorder
parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for
bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the
quartic cumulants at the critical point shows conclusively that these models
belong to the same universality class and allows us to estimate the
scaling-correction exponent omega related to the leading irrelevant operator,
omega=1.0(1). We also determine the critical exponents nu and eta. Taking into
account the scaling corrections, we obtain nu=2.53(8) and eta=-0.384(9).Comment: 9 pages, published versio
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 theories. We present an
overview of field-theoretical results obtained from the analysis of high-order
perturbative series in the frameworks of the 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() and
O() respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200
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 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 is estimated as
, while the magnetic susceptibility and magnetization
exponents and for Helium 3 are ,
.Comment: 19 pages, 4 fig
Critical behavior of the random-anisotropy model in the strong-anisotropy limit
We investigate the nature of the critical behavior of the random-anisotropy
Heisenberg model (RAM), which describes a magnetic system with random uniaxial
single-site anisotropy, such as some amorphous alloys of rare earths and
transition metals. In particular, we consider the strong-anisotropy limit
(SRAM), in which the Hamiltonian can be rewritten as the one of an Ising
spin-glass model with correlated bond disorder. We perform Monte Carlo
simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring
correlation functions of the replica-replica overlap, which is the order
parameter at a glass transition. The corresponding results show critical
behavior and finite-size scaling. They provide evidence of a finite-temperature
continuous transition with critical exponents and
. These results are close to the corresponding estimates that
have been obtained in the usual Ising spin-glass model with uncorrelated bond
disorder, suggesting that the two models belong to the same universality class.
We also determine the leading correction-to-scaling exponent finding .Comment: 24 pages, 13 figs, J. Stat. Mech. in pres
Universality class of 3D site-diluted and bond-diluted Ising systems
We present a finite-size scaling analysis of high-statistics Monte Carlo
simulations of the three-dimensional randomly site-diluted and bond-diluted
Ising model. The critical behavior of these systems is affected by
slowly-decaying scaling corrections which make the accurate determination of
their universal asymptotic behavior quite hard, requiring an effective control
of the scaling corrections. For this purpose we exploit improved Hamiltonians,
for which the leading scaling corrections are suppressed for any thermodynamic
quantity, and improved observables, for which the leading scaling corrections
are suppressed for any model belonging to the same universality class.
The results of the finite-size scaling analysis provide strong numerical
evidence that phase transitions in three-dimensional randomly site-diluted and
bond-diluted Ising models belong to the same randomly dilute Ising universality
class. We obtain accurate estimates of the critical exponents, ,
, , , ,
, and of the leading and next-to-leading correction-to-scaling
exponents, and .Comment: 45 pages, 22 figs, revised estimate of n
Irrelevant operators in the two-dimensional Ising model
By using conformal-field theory, we classify the possible irrelevant
operators for the Ising model on the square and triangular lattices. We analyze
the existing results for the free energy and its derivatives and for the
correlation length, showing that they are in agreement with the conformal-field
theory predictions. Moreover, these results imply that the nonlinear scaling
field of the energy-momentum tensor vanishes at the critical point. Several
other peculiar cancellations are explained in terms of a number of general
conjectures. We show that all existing results on the square and triangular
lattice are consistent with the assumption that only nonzero spin operators are
present.Comment: 32 pages. Added comments and reference
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