arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

At least 235 records · Page 13Linked to original sources

arXiv1997

Optimal Energy Estimation in Path-Integral Monte Carlo Simulations

We investigate the properties of two standard energy estimators used in path-integral Monte Carlo simulations. By disentangling the variance of the estimators and their autocorrelation times we analyse the dependence of the performance on the update algorithm and present a detailed comparison of refined update schemes such as multigrid and staging techniques. We show that a proper combination of the two estimators leads to a further reduction of the statistical error of the estimated energy with respect to the better of the two without extra cost.

cond-mat↗

arXiv1997

Monte Carlo Study of Pure-Phase Cumulants of 2D q-State Potts Models

We performed Monte Carlo simulations of the two-dimensional q-state Potts model with q=10, 15, and 20 to study the energy and magnetization cumulants in the ordered and disordered phase at the first-order transition point $β_t$. By using very large systems of size 300 x 300, 120 x 120, and 80 x 80 for q=10, 15, and 20, respectively, our numerical estimates provide practically (up to unavoidable, but very small statistical errors) exact results which can serve as a useful test of recent resummed large-q expansions for the energy cumulants by Bhattacharya `et al.' [J. Phys. I (France) 7 (1997) 81]. Up to the third order cumulant and down to q=10 we obtain very good agreement, and also the higher-order estimates are found to be compatible.

hep-lat↗

arXiv1996

Three-Dimensional 3-State Potts Model Revisited With New Techniques

We report a fairly detailed finite-size scaling analysis of the first-order phase transition in the three-dimensional 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed `only' by exponentially small terms. In these quantities no asymptotic power series in the inverse volume are involved which complicate the finite-size scaling behaviour of standard observables related to the specific-heat maxima or Binder-parameter minima. Introduced initially for strong first-order phase transitions in q-state Potts models with ``large enough'' q, the new techniques prove to be surprisingly accurate for a q value as small as 3. On the basis of the high-precision Monte Carlo data of Alves `et al.' [Phys. Rev. B43 (1991) 5846], this leads to a refined estimate of $β_t = 0.550,565(10)$ for the infinite-volume transition point.

hep-lat↗

arXiv1996

Computer Simulations of Quantum Chains

We report recent progress in computer simulations of quantum systems described in the path-integral formulation. For the example of the $ϕ^4$ quantum chain we show that the accuracy of the simulation may greatly be enhanced by a combination of multigrid update techniques with a refined discretization scheme. This allows us to assess the accuracy of a variational approximation.

cond-mat↗

arXiv1996

Convergence Behavior of Variational Perturbation Expansions

Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we explain the physical origin of the empirically observed convergence behavior which is exponentially fast with superimposed oscillations.

quant-ph↗

arXiv1996

Logarithmic Corrections in the 2D XY Model

Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square $L \times L$ lattices, the scaling behavior of the susceptibility $χ$ and correlation length $ξ$ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections $(ln L)^{-2r}$ in the finite-size scaling region and $(ln ξ)^{-2r}$ in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to $512^2$ we obtain $r = -0.0270(10)$, in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to $ξ\approx 140$ in the high-temperature phase, however, we arrive at quite a different estimate of $r = 0.0560(17)$, which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation.

hep-lat↗

arXiv1996

Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths

We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/ξ)$, where $ξ$ is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on large square lattices of size $300 \times 300$, $120 \times 120$, and $80 \times 80$, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length $ξ_d(β_t)$ in the disordered phase at the first-order transition point $β_t$ with an accuracy of about $1%-2%$ for all considered values of $q$. This is a considerable improvement over estimates derived from the large-distance behavior of standard (projected) two-point correlation functions, which are also discussed for comparison.

hep-lat↗

arXiv1996

Fixed versus random triangulations in 2D simplicial Regge calculus

We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the $dl/l$ measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random triangulations, which are obtained according to the standard Voronoi-Delaunay procedure. We compare both approaches quantitatively and show that the difference in the expectation value of $R^2$ between the fixed and the random triangulation depends on the lattice size and the surface area $A$. We also try again to measure the string susceptibility exponents through a finite-size scaling Ansatz in the expectation value of an added $R^2$ interaction term in an approach where $A$ is held fixed. The string susceptibility exponent $γ_{str}'$ is shown to agree with theoretical predictions for the sphere, whereas the estimate for $γ_{str}$ appears to be too negative.

hep-lat↗

arXiv1996

Critical Exponents of the Classical Heisenberg Ferromagnet

In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352, 1996) reported high precision Monte Carlo (MC) estimates of the static critical exponents of the classical 3D Heisenberg model, which stand in sharp contrast to values obtained by four independent approaches, namely by other recent high statistics MC simulations, high-temperature series analyses, field theoretical methods, and experimental studies. In reply to the above cited work we submitted this paper as a comment to Phys. Rev. Lett.

hep-lat↗

arXiv1996

Multigrid Method versus Staging Algorithm for PIMC Simulations

We present a comparison of the performance of two non-local update algorithms for path integral Monte Carlo (PIMC) simulations, the multigrid Monte Carlo method and the staging algorithm. Looking at autocorrelation times for the internal energy we show that both refined algorithms beat the slowing down which is encountered for standard local update schemes in the continuum limit. We investigate the conditions under which the staging algorithm performs optimally and give a brief discussion of the mutual merits of the two algorithms.

cond-mat↗

arXiv1995

Ising Spins on a Gravitating Sphere

We investigated numerically an Ising model coupled to two-dimensional Euclidean gravity with spherical topology, using Regge calculus with the $dl/l$ path-integral measure to discretize the gravitational interaction. Previous studies of this system with toroidal topology have shown that the critical behavior of the Ising model remains in the flat-space Onsager universality class, contrary to the predictions of conformal field theory and matrix models. Implementing the spherical topology as triangulated surfaces of three-dimensional cubes, we find again strong evidence that the critical exponents of the Ising transition are consistent with the Onsager values, and that KPZ exponents are definitely excluded.

hep-lat↗

arXiv1995

Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach

We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with $R^2$-interaction on spherical topologies, employing Regge's formulation. We attempt to measure the string susceptibility exponent $γ_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$, as has been done in a previous study by Bock and Vink ( hep-lat/9406018 ). By considerably extending the range and statistics of their study we find that this Ansatz is plagued by large systematic errors. The $R^2$ specific string susceptibility exponent $\GS'$ is found to agree with theoretical predictions, but its determination also is subject to large systematic errors and the presence of finite-size scaling corrections. To circumvent this obstacle we suggest a new scaling Ansatz which in principle should be able to predict both, $\GS$ and $\GS'$. First results indicate that this requires large system sizes to reduce the uncertainties in the finite-size scaling Ansätze. Nevertheless, our investigation shows that within the achievable accuracy the numerical estimates are still compatible with analytic predictions, contrary to the recent claim by Bock and Vink.

hep-lat↗

arXiv1995

Monte Carlo Study of 8-State Potts Model on 2D Random Lattices

We study the effect of quenched coordination-number disorder of random lattices on the nature of the phase transition in the two-dimensional eight-state Potts model, which is of first order on regular lattices. We consider Poissonian random lattices of toroidal topology constructed according to the Voronoi/Delaunay prescription. Monte Carlo simulations yield strong evidence that the phase transition remains first order.

hep-lat↗

arXiv1995

Correlation Length From Cluster-Diameter Distribution

We report numerical estimates of correlation lengths in 2D Potts models from the asymptotic decay of the cluster-diameter distribution. Using this observable we are able to verify theoretical predictions for the correlation length in the disordered phase at the transition point for $q=10$, 15, and 20 with an accuracy of about $1%-2%$. This is a considerable improvement over previous measurements using the standard (projected) two-point function.

hep-lat↗

arXiv1995

2D Potts Model Correlation Lengths: Numerical Evidence for $ξ_o = ξ_d$ at $β_t$

We have studied spin-spin correlation functions in the ordered phase of the two-dimensional $q$-state Potts model with $q=10$, 15, and 20 at the first-order transition point $β_t$. Through extensive Monte Carlo simulations we obtain strong numerical evidence that the correlation length in the ordered phase agrees with the exactly known and recently numerically confirmed correlation length in the disordered phase: $ξ_o(β_t) = ξ_d(β_t)$. As a byproduct we find the energy moments in the ordered phase at $β_t$ in very good agreement with a recent large $q$-expansion.

hep-lat↗

arXiv1995

New results on $γ_{\rm str}$ in 2D quantum gravity using Regge calculus

We study 2D quantum gravity on spherical topologies using the Regge calculus approach. Our goal is to shed new light upon the validity of the Regge approach to quantum gravity, which has recently been questioned in the literature. We incorporate an $R^2$ interaction term and investigate its effect on the value of the string susceptibility exponent $γ_{\rm str}$ using two different finite-size scaling Ansätze. Our results suggest severe shortcomings of the methods used so far to determine $\GS$ and show a possible cure of the problems. To have better control over the influence of irregular vertices, we choose besides the almost regular triangulation of the sphere as the surface of a cube a random triangulation according to the Voronoi-Delaunay prescription.

hep-lat↗

arXiv1995

Two-Dimensional 8-State Potts Model on Random Lattices: A Monte Carlo Study

We use two-dimensional Poissonian random lattices of Voronoi/ Delaunay type to study the effect of quenched coordination number randomness on the nature of the phase transition in the eight-state Potts model, which is of first order on regular lattices. From extensive Monte Carlo simulations we obtain strong evidence that the phase transition remains first order for this type of quenched randomness. Our result is in striking contrast to a recent Monte Carlo study of quenched bond randomness for which the order of the phase transition changes from first to second order.

hep-lat↗

arXiv1995

Measure dependence of 2D simplicial quantum gravity

We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $γ_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.

hep-lat↗