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 $z$.Comment: 11 pages, 13 figures, accepted for publication in Phys. Rev.

Rational vs Polynomial Character of Wnl_n^l-Algebras

The constraints proposed recently by Bershadsky to produce $W^l_n$ 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

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

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

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

Discovery of molecular gas around HD 131835 in an APEX molecular line survey of bright debris disks

Debris disks are considered to be gas-poor, but recent observations revealed molecular or atomic gas in several 10-40 Myr old systems. We used the APEX and IRAM 30m radiotelescopes to search for CO gas in 20 bright debris disks. In one case, around the 16 Myr old A-type star HD 131835, we discovered a new gas-bearing debris disk, where the CO 3-2 transition was successfully detected. No other individual system exhibited a measurable CO signal. Our Herschel Space Observatory far-infrared images of HD 131835 marginally resolved the disk both at 70 and 100$\mu$m, with a characteristic radius of ~170 au. While in stellar properties HD 131835 resembles $\beta$ Pic, its dust disk properties are similar to those of the most massive young debris disks. With the detection of gas in HD 131835 the number of known debris disks with CO content has increased to four, all of them encircling young ($\leq$40 Myr) A-type stars. Based on statistics within 125 pc, we suggest that the presence of detectable amount of gas in the most massive debris disks around young A-type stars is a common phenomenon. Our current data cannot conclude on the origin of gas in HD 131835. If the gas is secondary, arising from the disruption of planetesimals, then HD 131835 is a comparably young and in terms of its disk more massive analogue of the $\beta$ Pic system. However, it is also possible that this system similarly to HD 21997 possesses a hybrid disk, where the gas material is predominantly primordial, while the dust grains are mostly derived from planetesimals.Comment: Accepted for publication in ApJ, 18 pages, 9 figures, 5 table