arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

247 records · Page 14Linked to original sources

arXiv1995

The Ising transition in 2D simplicial quantum gravity - can Regge calculus be right?

We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to $512^2$ vertices. For the constant area ensemble and the $dl/l$ functional measure we definitively can exclude the critical exponents of the Ising phase transition as predicted for dynamically triangulated surfaces. We rather find clear evidence that the critical exponents agree with the Onsager values for static regular lattices, independent of the coupling strength of an $R^2$ interaction term. For exploratory simulations using the lattice version of the Misner measure the situation is less clear.

hep-lat↗

arXiv1994

Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional $ϕ^4$-Model: Autocorrelations and Interface Tension

We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar $ϕ^4$-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.

hep-lat↗

arXiv1994

Monte Carlo simulation of $1+1$-dimensional $ϕ^4$ quantum field theory

We report results of a Monte Carlo simulation of the $ϕ^4$ quantum field theory using multigrid simulation techniques and a refined discretization scheme. The resulting accuracy of our data allows for a significant test of an analytical approximation based on a variational ansatz. While the variational approximation is well reproduced for a large range of parameters we find significant deviations for low temperatures and large couplings.

hep-lat↗

arXiv1994

Test of variational approximation for $phi^4$ quantum chain by Monte Carlo simulation

We report results of a Monte Carlo simulation of the $ϕ^4$ quantum chain. In order to enhance the efficiency of the simulation we combine multigrid simulation techniques with a refined discretization scheme. The resulting accuracy of our data allows for a significant test of an analytical approximation based on a variational ansatz. While the variational approximation is well reproduced for a large range of parameters we find significant deviations for low temperatures and large couplings.

cond-mat↗

arXiv1994

Ordered vs Disordered: Correlation Lengths of 2D Potts Models at β_t

We performed Monte Carlo simulations of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ and measured the spin-spin correlation function at the first-order transition point $β_t$ in the disordered and ordered phase. Our results for the correlation length $ξ_d(β_t)$ in the disordered phase are compatible with an analytic formula. Estimates of the correlation length $ξ_o(β_t)$ in the ordered phase yield strong numerical evidence that $R \equiv ξ_o(β_t)/ξ_d(β_t) = 1$.

hep-lat↗

arXiv1994

Multibondic Cluster Algorithm

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with $q=7, 10$ and $20$ show that the autocorrelation times of this algorithm grow with the system size $V$ as $τ\propto V^α$, where the exponent takes the optimal random walk value of $α\approx 1$.

hep-lat↗

arXiv1994

Recent Developments in Monte Carlo Simulations of First-Order Phase Transitions

In the past few years considerable progress has been made in Monte Carlo simulations of first-order phase transitions and in the analysis of the resulting finite-size data. In this paper special emphasis will be placed on multicanonical simulations using multigrid update techniques, on numerical estimates of interface tensions, and on accurate methods for determining the transition point and latent heat.

hep-lat↗

arXiv1994

Correlation Function at $β_t$ in the Disordered Phase of 2D Potts Models

We use Monte Carlo simulations to measure the spin-spin correlation function in the disordered phase of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ at the first-order transition point $β_t$. To extract the correlation length $ξ_d$ from the exponential decay of the correlation function over several decades with the desired accuracy we make extensively use of cluster-update techniques and improved estimators. Our results for $ξ_d$ are compatible with an analytic formula. As a byproduct we also measure the energy moments in the disordered phase and find very good agreement with a recent large $q$ expansion at $β_t$.

hep-lat↗

arXiv1994

Multibondic Cluster Algorithm for Monte Carlo Simulations of First-Order Phase Transitions

hep-lat↗

arXiv1993

Monte Carlo Study of Topological Defects in the 3D Heisenberg Model

We use single-cluster Monte Carlo simulations to study the role of topological defects in the three-dimensional classical Heisenberg model on simple cubic lattices of size up to $80^3$. By applying reweighting techniques to time series generated in the vicinity of the approximate infinite volume transition point $K_c$, we obtain clear evidence that the temperature derivative of the average defect density $d\langle n \rangle/dT$ behaves qualitatively like the specific heat, i.e., both observables are finite in the infinite volume limit. This is in contrast to results by Lau and Dasgupta [{\em Phys. Rev.\/} {\bf B39} (1989) 7212] who extrapolated a divergent behavior of $d\langle n \rangle/dT$ at $K_c$ from simulations on lattices of size up to $16^3$. We obtain weak evidence that $d\langle n \rangle/dT$ scales with the same critical exponent as the specific heat.As a byproduct of our simulations, we obtain a very accurate estimate for the ratio $α/ν$ of the specific-heat exponent with the correlation-length exponent from a finite-size scaling analysis of the energy.

hep-lat↗

arXiv1993

Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents $ν,α,β,γ, η$ from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to $100^3$ spins. This enables us to compute independent estimates of $ν$ and $γ$ from power-law fits of their critical divergencies.

hep-lat↗

arXiv1992

Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg Model

We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.

hep-lat↗

arXiv1992

Monte Carlo Calculation of the Surface Free Energy for the 2d 7-state Potts Model, and an Estimate for 4d SU(3) Gauge Theory

Using the recently proposed multicanonical ensemble, we perform Monte Carlo simulation for the 2d 7-state Potts model and calculate its surface free energy density (surface tension) to be $2 f^s = 0.0241 \pm 0.0010$. This is an order of magnitude smaller than other estimates in the recent literature. Relying on existing Monte Carlo data, we also give a preliminary estimate for the surface tension of 4d SU(3) lattice gauge theory with $L_t=2$.

hep-lat↗