Steffen Meyer

Critical exponents of the 3D XY model from cluster update Monte Carlo

Abstract We present results of a study of the three-dimensional XY model using a cluster updating algorithm with improved estimators, which enables us to perform simulations with greatly increased efficiency. Critical slowing down is drastically reduced and the dynamical critical exponent is found to be zcl = 0.46 ± 0.03. We obtain for the critical coupling Kc = 0.45421 ± 0.00008 and for th susceptibility exponent γ = 1.327 ± 0.008. These results are consistent with the XY model being the same universality class as the three-state antiferromagnetic Potts model.

submitter : Critical behaviour of the 3D XY-model: A Monte Carlo study

We present the results of a study of the three-dimensional XY-model using the single cluster updating algorithm combined with improved estimators. We have measured the susceptibility and the correlation length for various couplings in the high temperature phase on lattices of size up to 1123. In the neighbourhood of the critical temperature we studied the Binder-cumulant and other cumulant like quantities on lattices of size up to 643. From our accurate numerical data we obtain for the critical coupling Kc = 0.45420(2), for the static critical exponents γ/ν = 1.975(6), ν = 0.662(7) at criticality and for the susceptibility exponent γ = 1.324(1) in the high temperature phase.

First order phase transitions in SU(2) gauge theories with many flavours of staggered fermions

Abstract We present a hybrid Monte Carlo study of SU(2) lattice gauge theory coupled to 8 and 12 flavours of staggered fermions. The chiral and deconfinement phase transitions are coincident on 6 4 and 8 4 lattices. For N f = 8 there are large finite size effects suggesting a temperature driven transition induced by the finite size of the system. With this assumption, aT c does not satisfy asymptotic scaling. For 12 flavours, asymptotic freedom is lost and we expect a bulk transition on a sufficiently large lattice; our numerical results for the critical point with N f = 12 show large finite size effects. Evidence for the first order nature of the transitions derives from the observation of tunneling between metastable states.

Noncritical multigrid Monte Carlo: O(3) non-linear σ model

Abstract We describe a multigrid Monte Carlo technique for asymptotically free lattice field theories like the O ( n ) non-linear σ model and the SU ( N ) × SU ( N ) chiral model in two dimensions. We study this multigrid Monte Carlo algorithm with a smooth interpolation operator in the two-dimensional O (3) σ-model. On lattices up to 256 × 256 we achieve almost complete elimination of critical slowing down. With piecewise-constant interpolation we find a remaining critical slowing down with a dynamic critical exponent of z ≈ 1.

Does the topological charge scale in the lattice CP3-model?☆

Abstract Using a multigrid Monte Carlo algorithm with piecewise-linear interpolation operator for the two dimensional lattice CP 3 model with the standard quadratic action, we compare our results for the correlation length and the topological susceptibility with recent overrelaxation data. We do not confirm the scaling for the universal topological susceptibility found for smaller correlation length in the overrelaxation simulation. We find clear evidence that a single state saturates the 2-point correlation function at large distances.

Critical exponents and finite-size effects at the chiral transition in the SU(2) Higgs model

Abstract A detailed comparison is made between results of a hybrid Monte Carlo simulation and mean-field theory for the chiral phase transition in the SU(2) Higgs model with dynamical fermions. It is shown that mean-field theory accounts well for the data as well as for the observed finite-size effects. Thus we are able to make inferences about the infinite volume limit without ad hoc extrapolations.

The chiral transition in the SU(2) Higgs model at weak coupling

Abstract We study the phase structure of the SU(2) gauge Higgs model with staggered fermions using the hybrid Monte Carlo algorithm on 6 4 and 8 4 lattices. At weak coupling there is a single Higgs chiral transition, which is most likely first order. There is no evidence for the confining chirally symmetric phase required for the strongly coupled standard model of Abbott and Farhi.

Multigrid acceleration for asymptotically free theories

Abstract We present a multigrid Monte Carlo algorithm with piecewise-linear interpolation operator for nonlinear σ models with global chiral SU ( N ) × SU ( N ) symmetry or CP N −1 manifold. We demonstrate its efficiency in the two dimensional SU (3) × SU (3) chiral model and the CP 3 nonlinear σ model for correlation length up to 77 in lattice units. On lattices up to size 512 × 512 we achieve almost complete elimination of critical slowing down in the CP 3 case, with a dynamical critical exponent z MGMC = 0.2 ± 0.1. Asymptotic scaling with the bare coupling does not appear to set in for the standard action of both models in the range of parameters studied.

Phase transitions in SU(2) gauge theory with many flavours of staggered fermions

Abstract We present a Hybrid Monte Carlo study of SU(2) lattice gauge theory with 8 and 12 flavours of staggered fermions. The chiral and deconfinement phase transitions coincide on 6 4 and 8 4 lattices. For N f = 8 there are large finite size effects suggesting that these are temperature driven transitions induced by the finite size of the system. With this assumption, aT c does not satisfy asymptotic scaling. For N f = 12, the finite size effects are still large even though we expect a bulk transition for this non-asymptotically-free theory. Some evidence for the first order nature of the transitions comes from the observation of tunnelling between metastable states.