1,267 research outputs found
Deconfinement transition in 2+1-dimensional SU(4) lattice gauge theory
A missing piece is added to the Svetitsky-Yaffe conjecture. The spin model in
the same universality class as the (2+1)d SU(4) theory, the 2d Ashkin-Teller
model, has a line of continuously varying critical exponents. The exponents
measured in the gauge theory correspond best to the Potts point on the
Ashkin-Teller line.Comment: Lattice2003(topology), 3 pages, 5 figure
Graphical Representations for Ising Systems in External Fields
A graphical representation based on duplication is developed that is suitable
for the study of Ising systems in external fields. Two independent replicas of
the Ising system in the same field are treated as a single four-state
(Ashkin-Teller) model. Bonds in the graphical representation connect the
Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is
characterized by percolation in this representation. The representation leads
immediately to cluster algorithms; some applications along these lines are
discussed.Comment: 13 pages amste
Dynamic Critical Behavio(u)r of a Cluster Algorithm for the Ashkin--Teller Model
We study the dynamic critical behavior of a Swendsen--Wang--type algorithm
for the Ashkin--Teller model. We find that the Li--Sokal bound on the
autocorrelation time ()
holds along the self-dual curve of the symmetric Ashkin--Teller model, but this
bound is apparently not sharp. The ratio
appears to tend to infinity either as a logarithm or as a small power (0.05
\ltapprox p \ltapprox 0.12).Comment: 51062 bytes uuencoded gzip'ed (expands to 111127 bytes Postscript); 4
pages including all figures; contribution to Lattice '9
Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model
We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for
the Ashkin--Teller model. We find that the Li--Sokal bound on the
autocorrelation time ()
holds along the self-dual curve of the symmetric Ashkin--Teller model, and is
almost but not quite sharp. The ratio appears
to tend to infinity either as a logarithm or as a small power (). In an appendix we discuss the problem of extracting estimates of
the exponential autocorrelation time.Comment: 59 pages including 3 figures, uuencoded g-compressed ps file.
Postscript size = 799740 byte
Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study
The critical behaviour of a bond-disordered Ashkin-Teller model on a square
lattice is investigated by intensive Monte-Carlo simulations. A duality
transformation is used to locate a critical plane of the disordered model. This
critical plane corresponds to the line of critical points of the pure model,
along which critical exponents vary continuously. Along this line the scaling
exponent corresponding to randomness varies continuously
and is positive so that randomness is relevant and different critical behaviour
is expected for the disordered model. We use a cluster algorithm for the Monte
Carlo simulations based on the Wolff embedding idea, and perform a finite size
scaling study of several critical models, extrapolating between the critical
bond-disordered Ising and bond-disordered four state Potts models. The critical
behaviour of the disordered model is compared with the critical behaviour of an
anisotropic Ashkin-Teller model which is used as a refference pure model. We
find no essential change in the order parameters' critical exponents with
respect to those of the pure model. The divergence of the specific heat is
changed dramatically. Our results favor a logarithmic type divergence at
, for the random bond Ashkin-Teller and four state Potts
models and for the random bond Ising model.Comment: RevTex, 14 figures in tar compressed form included, Submitted to
Phys. Rev.
Spin interfaces in the Ashkin-Teller model and SLE
We investigate the scaling properties of the spin interfaces in the
Ashkin-Teller model. These interfaces are a very simple instance of lattice
curves coexisting with a fluctuating degree of freedom, which renders the
analytical determination of their exponents very difficult. One of our main
findings is the construction of boundary conditions which ensure that the
interface still satisfies the Markov property in this case. Then, using a novel
technique based on the transfer matrix, we compute numerically the left-passage
probability, and our results confirm that the spin interface is described by an
SLE in the scaling limit. Moreover, at a particular point of the critical line,
we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex
model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure
Emerging criticality in the disordered three-color Ashkin-Teller model
We study the effects of quenched disorder on the first-order phase transition
in the two-dimensional three-color Ashkin-Teller model by means of large-scale
Monte Carlo simulations. We demonstrate that the first-order phase transition
is rounded by the disorder and turns into a continuous one. Using a careful
finite-size-scaling analysis, we provide strong evidence for the emerging
critical behavior of the disordered Ashkin-Teller model to be in the clean
two-dimensional Ising universality class, accompanied by universal logarithmic
corrections. This agrees with perturbative renormalization-group predictions by
Cardy. As a byproduct, we also provide support for the strong-universality
scenario for the critical behavior of the two-dimensional disordered Ising
model. We discuss consequences of our results for the classification of
disordered phase transitions as well as generalizations to other systems.Comment: 18 pages, 18 eps figures included, final version as publishe
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