402 research outputs found
Frustrated magnets in three dimensions: a nonperturbative approach
Frustrated magnets exhibit unusual critical behaviors: they display scaling
laws accompanied by nonuniversal critical exponents. This suggests that these
systems generically undergo very weak first order phase transitions. Moreover,
the different perturbative approaches used to investigate them are in conflict
and fail to correctly reproduce their behavior. Using a nonperturbative
approach we explain the mismatch between the different perturbative approaches
and account for the nonuniversal scaling observed.Comment: 7 pages, 1 figure. IOP style files included. To appear in Journal of
Physics: Condensed Matter. Proceedings of the conference HFM 2003, Grenoble,
Franc
Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group
We study the critical behavior of frustrated systems by means of Pade-Borel
resummed three-loop renormalization-group expansions and numerical Monte Carlo
simulations. Amazingly, for six-component spins where the transition is second
order, both approaches disagree. This unusual situation is analyzed both from
the point of view of the convergence of the resummed series and from the
possible relevance of non perturbative effects.Comment: RevTex, 10 pages, 3 Postscript figure
The critical behavior of frustrated spin models with noncollinear order
We study the critical behavior of frustrated spin models with noncollinear
order, including stacked triangular antiferromagnets and helimagnets. For this
purpose we compute the field-theoretic expansions at fixed dimension to six
loops and determine their large-order behavior. For the physically relevant
cases of two and three components, we show the existence of a new stable fixed
point that corresponds to the conjectured chiral universality class. This
contradicts previous three-loop field-theoretical results but is in agreement
with experiments.Comment: 4 pages, RevTe
Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral model
With the help of the improved Monte Carlo renormalization-group scheme, we
numerically investigate the renormalization group flow of the antiferromagnetic
Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and
its effective Hamiltonian, 2N-component chiral model which is used in
the field-theoretical studies. We find that the XY-STA model with the lattice
size exhibits clear first-order behavior. We also
find that the renormalization-group flow of STA model is well reproduced by the
chiral model, and that there are no chiral fixed point of
renormalization-group flow for N=2 and 3 cases. This result indicates that the
Heisenberg-STA model also undergoes first-order transition.Comment: v1:15 pages, 15 figures v2:updated references v3:added comments on
the higher order irrelevant scaling variables v4:added results of larger
sizes v5:final version to appear in J.Phys.Soc.Jpn Vol.72, No.
Reaction Networks For Interstellar Chemical Modelling: Improvements and Challenges
We survey the current situation regarding chemical modelling of the synthesis
of molecules in the interstellar medium. The present state of knowledge
concerning the rate coefficients and their uncertainties for the major
gas-phase processes -- ion-neutral reactions, neutral-neutral reactions,
radiative association, and dissociative recombination -- is reviewed. Emphasis
is placed on those reactions that have been identified, by sensitivity
analyses, as 'crucial' in determining the predicted abundances of the species
observed in the interstellar medium. These sensitivity analyses have been
carried out for gas-phase models of three representative, molecule-rich,
astronomical sources: the cold dense molecular clouds TMC-1 and L134N, and the
expanding circumstellar envelope IRC +10216. Our review has led to the proposal
of new values and uncertainties for the rate coefficients of many of the key
reactions. The impact of these new data on the predicted abundances in TMC-1
and L134N is reported. Interstellar dust particles also influence the observed
abundances of molecules in the interstellar medium. Their role is included in
gas-grain, as distinct from gas-phase only, models. We review the methods for
incorporating both accretion onto, and reactions on, the surfaces of grains in
such models, as well as describing some recent experimental efforts to simulate
and examine relevant processes in the laboratory. These efforts include
experiments on the surface-catalysed recombination of hydrogen atoms, on
chemical processing on and in the ices that are known to exist on the surface
of interstellar grains, and on desorption processes, which may enable species
formed on grains to return to the gas-phase.Comment: Accepted for publication in Space Science Review
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.Comment: 45 pages, 20 figs, some additions, Phys.Rev.B in pres
Critical thermodynamics of three-dimensional chiral model for N > 3
The critical behavior of the three-dimensional -vector chiral model is
studied for arbitrary . The known six-loop renormalization-group (RG)
expansions are resummed using the Borel transformation combined with the
conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point
location and the structure of RG flows, it is found that two marginal values of
exist which separate domains of continuous chiral phase transitions and where such
transitions are first-order. Our calculations yield and
. For the structure of RG flows is identical to
that given by the and 1/N expansions with the chiral fixed point
being a stable node. For the chiral fixed point turns out to be a
focus having no generic relation to the stable fixed point seen at small
and large . In this domain, containing the physical values and , phase trajectories approach the fixed point in a spiral-like
manner giving rise to unusual crossover regimes which may imitate varying
(scattered) critical exponents seen in numerous physical and computer
experiments.Comment: 12 pages, 3 figure
Phase Transition of XY Model in Heptagonal Lattice
We numerically investigate the nature of the phase transition of the XY model
in the heptagonal lattice with the negative curvature, in comparison to other
interaction structures such as a flat two-dimensional (2D) square lattice and a
small-world network. Although the heptagonal lattice has a very short
characteristic path length like the small-world network structure, it is
revealed via calculation of the Binder's cumulant that the former exhibits a
zero-temperature phase transition while the latter has the finite-temperature
transition of the mean-field nature. Through the computation of the vortex
density as well as the correlation function in the low-temperature
approximation, we show that the absence of the phase transition originates from
the strong spinwave-type fluctuation, which is discussed in relation to the
usual 2D XY model.Comment: 5 pages, 6 figures, to be published in Europhys. Let
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