Mihail Marcu

Stochastic cluster algorithms for discrete gaussian (SOS) models

Abstract We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z . Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm.

Cluster algorithm for a solid-on-solid model with constraints

We adapt a cluster algorithm devised by us for simulations of solid-on-solid (SOS) models, to the body-centered SOS model. We note that this work is an application of a cluster algorithm on a model with constraints. The performance of this algorithm is studied in detail in both phases of the model, including a finite-size scaling analysis of the autocorrelations, and we find that critical slowing down is significantly reduced

CLUSTER ALGORITHMS FOR SURFACES

We discuss a new cluster algorithm that completely eliminates critical slowing down for surface models of the SOS (solid-on-solid) type.

Proof of universal perimeter law behaviour of the Wegner-Wilson loop in nonabelian lattice gauge theories with Higgs Fields

Abstract By an application of reflection positivity with respect to oblique lattice planes it is proven that in lattice gauge theories with scalar matter fields the Wegner-Wilson loop is bounded from below by exp (-const. perimeter).

Monte Carlo simulation of 2D quantum gravity as open dynamically triangulate random surfaces

We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to fluctuate. The algorithm works in the presence of matter fields. We here present results for the pure gravity case. The algorithm reproduces the theoretical expectations.

High precision verification of the Kosterlitz thouless scenario

Abstract We verify the Kosterlitz Thouless scenario for three different SOS (solid-on-solid) models, including the dual transforms of XY -models with Villain and with cosine action. The method is based on a matching of the renormalization group (RG) flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. We obtain high precision estimates for the critical couplings and other non-universal quantities.

Dual interpretation of order parameters for lattice gauge theories with matter fields

Abstract A dual interpretation of the vacuum overlap order parameter (VOOP) and of the flux correlations order parameter (FCOP) is presented. For the FCOP we interchange one of the space dimensions with the euclidean time. In 3 + 1 dimensions the resulting quantity is interpreted as the vacuum overlap of a magnetic vortex, i.e. of a gauge-invariant energy-regularized state containing a closed line of center-magnetic flux. In the confinement region the vortices are condensed in the vacuum. In the Higgs region only vortices of small size exist as excitations. The screening length for dynamical center-electric charge fluctuations can be reinterpreted as the characteristic length for vortex fragmentation. The vacuum correlations responsible for the existence of magnetic vortices as excitations are measured by a (purely spatial) quantity obtained from the VOOP by replacing the time direction with a spatial one. At finite temperatures this quantity can be used as an order parameter for the symmetry restauration transition. In 2 + 1 dimensions the dual interpretation of our order parameters is simpler: we just interchange VOOP and FCOP, states with center-electric charge and states carrying center-magnetic charge (monopoles), the confinement and the Higgs region.

A numerical study of the SU(2) Higgs model

Abstract Preliminary results of a simulation of the SU(2) theory with a Higgs field in the fundamental representation are presented. For an 8 3 × 16 and a 12 3 × 24 lattice we investigated the parameter range 2.4 ≤ β ≤ 3.0, λ = ∞. In the confinement region huge autocorrelations prevent us from obtaining reliable results. In the Higgs region the W mass m w turns out to have larger finite size effects than previously expected. Besides the W and Higgs masses, we estimate for β = 3.0 on the 12 3 × 24 lattice the renormalized gauge coupling g т and (unfortunately only up to an unknown waave function renormalization) the Higgs expectation value ν. The latter is obtained from the vacuum overlap order parameter. Technical problems encountered in its computation are discussed in some detail. Finally we discuss our results; in particular we show that the tree level relation m w 2 = g τ 2 ν 2 /2 is fulfilled remarkably well.

Surface simulations without critical slowing down

Abstract We present new Monte Carlo cluster algorithms which eliminate critical slowing down in surface models of the solid-on-solid type. The algorithms are based on reflecting parts of the surface with respect to appropriately chosen planes. The proper choice of the reflection plane turns out to be crucial.

Towards a better quantitative understanding of the SU(2) Higgs model

Abstract We describe the results of a high-statistics simulation of the SU(2) Higgs model at λ=∞, β=2.4, 2.7 and 3.0, on lattices of sizes ranging between 83×16 and 143×28. The measured quantities are the Higgs and W masses, the potential between two static sources from which the renormalized gauge coupling is extracted, and the vacuum overlap order parameter which defines the Higgs expectation value in a gauge invariant way. Strong finite-size effects are observed. They seem to come under control for the larger lattices, at least at β=2.7. Renormalized tree level relations are found to hold remarkably well at β=2.7 and 3.0.