726 research outputs found
Equilibriumlike invaded cluster algorithm: critical exponents and dynamical properties
We present a detailed study of the Equilibriumlike invaded cluster algorithm
(EIC), recently proposed as an extension of the invaded cluster (IC) algorithm,
designed to drive the system to criticality while still preserving the
equilibrium ensemble. We perform extensive simulations on two special cases of
the Potts model and examine the precision of critical exponents by including
the leading corrections. We show that both thermal and magnetic critical
exponents can be obtained with high accuracy compared to the best available
results. The choice of the auxiliary parameters of the algorithm is discussed
in context of dynamical properties. We also discuss the relation to the
Li-Sokal bound for the dynamical exponent .Comment: 11 pages, 13 figures, accepted for publication in Phys. Rev.
Rational vs Polynomial Character of W-Algebras
The constraints proposed recently by Bershadsky to produce algebras
are a mixture of first and second class constraints and are degenerate. We show
that they admit a first-class subsystem from which they can be recovered by
gauge-fixing, and that the non-degenerate constraints can be handled by
previous methods. The degenerate constraints present a new situation in which
the natural primary field basis for the gauge-invariants is rational rather
than polynomial. We give an algorithm for constructing the rational basis and
converting the base elements to polynomials.Comment: 18 page
Invaded cluster algorithm for a tricritical point in a diluted Potts model
The invaded cluster approach is extended to 2D Potts model with annealed
vacancies by using the random-cluster representation. Geometrical arguments are
used to propose the algorithm which converges to the tricritical point in the
two-dimensional parameter space spanned by temperature and the chemical
potential of vacancies. The tricritical point is identified as a simultaneous
onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of
"geometrical disorder cluster". The location of the tricritical point and the
concentration of vacancies for q = 1, 2, 3 are found to be in good agreement
with the best known results. Scaling properties of the percolating scaling
cluster and related critical exponents are also presented.Comment: 8 pages, 5 figure
The Three-Magnon Contribution to the Spin Correlation Function in Integer-Spin Antiferromagnetic Chains
The exact form factor for the O(3) non-linear sigma model is used to predict
the three-magnon contribution to the spin correlation function, S(q,w), near
wavevector q=pi in an integer spin, one-dimensional antiferromagnet. The
three-magnon contribution is extrememly broad and extremely weak; the
integrated intensity is <2% of the single-magnon contribution.Comment: 4 pages, 1 figur
Geometry of W-algebras from the affine Lie algebra point of view
To classify the classical field theories with W-symmetry one has to classify
the symplectic leaves of the corresponding W-algebra, which are the
intersection of the defining constraint and the coadjoint orbit of the affine
Lie algebra if the W-algebra in question is obtained by reducing a WZNW model.
The fields that survive the reduction will obey non-linear Poisson bracket (or
commutator) relations in general. For example the Toda models are well-known
theories which possess such a non-linear W-symmetry and many features of these
models can only be understood if one investigates the reduction procedure. In
this paper we analyze the SL(n,R) case from which the so-called W_n-algebras
can be obtained. One advantage of the reduction viewpoint is that it gives a
constructive way to classify the symplectic leaves of the W-algebra which we
had done in the n=2 case which will correspond to the coadjoint orbits of the
Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov
algebra. Our method in principle is capable of constructing explicit
representatives on each leaf. Another attractive feature of this approach is
the fact that the global nature of the W-transformations can be explicitly
described. The reduction method also enables one to determine the ``classical
highest weight (h. w.) states'' which are the stable minima of the energy on a
W-leaf. These are important as only to those leaves can a highest weight
representation space of the W-algebra be associated which contains a
``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter
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