arXiv subjects

M. Hasenbusch

Publications and source records attributed to M. Hasenbusch.

At least 55 records · Page 3Linked to original sources

arXiv1997

Monte-carlo renormalization group study of gauged RP(2) spin models in two dimensions

The 2D RP(2) gauge model is studied using the Monte-Carlo Renormalization Group. We confirm the first-order transition reported by Solomon et al. (PL 112B, (1982)) ending in a critical point associated with vorticity. We find evidence for a new renormalized trajectory which is responsible for a cross-over from the vortex dominated regime to the O(3) regime as the coupling is reduced. Near to the cross-over region a good signal for scaling will be observed in RP(2) but this is illusory and is due to the proximity of the new renormalized trajectory. We suggest that this is the origin of the `pseudo'-scaling observed Hasenbusch and Horgan (PR D53, (1996)). We find that the continuum limit of RP(2) is controlled by the O(3) fixed point. It is unclear whether the continuum limit of the new renormalized trajectory can be taken at the observed critical point.

hep-lat↗

arXiv1997

Universal Amplitude Ratios in the 3D Ising Model

We present a high precision Monte Carlo study of various universal amplitude ratios of the three dimensional Ising spin model. Using state of the art simulation techniques we studied the model close to criticality in both phases. Great care was taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain $C_+/C_-=4.75(3)$, $f_{+,2nd}/f_{-,2nd}=1.95(2)$ and $u^*=14.3(1)$. Our results are compatible with those obtained by field theoretic methods applied to the $ϕ^4$ theory and high and low temperature series expansions of the Ising model.

hep-lat↗

arXiv1997

Spectrum of the gauge Ising model in three dimensions

We present a high precision Monte Carlo study of the spectrum of the Ising gauge theory in three dimensions in the confining phase. Using state of the art Monte Carlo techniques we are able to accurately determine up to three masses in a single channel. We compare our results with the SU(2) spectrum and with the prediction of the Isgur-Paton model. Our data strongly support the conjecture that the glueball spectrum is described by some type of flux tube model. We also compare the spectrum with some recent results for the correlation length in the 3d spin Ising model. This analysis sheds light on some nontrivial features of the duality transformation.

hep-lat↗

arXiv1997

New Estimates On Various Critical/Universal Quantities of the 3D Ising Model

We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.

hep-lat↗

arXiv1997

A_+/A_-, alpha, nu, and f_s xi^3 from 3D Ising Energy and Specific Heat

We analyse Monte Carlo data for the energy and specific heat at and close to the critical point of the 3D cubic Ising model. From the finite size scaling of the energy E and the specific heat C at criticality we obtain the estimate nu = 0.6308(10). Furthermore, one obtains precise estimates for the ``backgrounds'' (nonsingular parts) E_ns and C_ns. Fitting solely off critical energy estimates to a scaling law, we find depending on the choice of the reduced temperature, either A_+/A_- = 0.550(12) and alpha=0.1115(37), or A_+/A_- = 0.567(16) and alpha=0.1047(48). Including information from the data at T_c, we obtain the estimate A_+/A_- = 0.560(10). We also determine the universal combination f_s xi^3 in both phases.

cond-mat.stat-mech↗

arXiv1997

The Interface Tension of the 3-Dimensional Ising Model in the Scaling Region

Using the Monte Carlo method, we determine the free energy of the interface of the 3D Ising model in the scaling region. By integrating the interface energies over the inverse temperature $β$, we obtain estimates for the free energies of interfaces with cross sections up to 96 by 96, and for a range $0.223 \leq β\leq 0.23$. Our data yield a precise estimation of the interface tensions $σ$. We determine the amplitude $σ_0$ in the critical law $σ\sim σ_0 t^μ$ and estimate the combination $σξ^2$ which yields the universal constant $R_{-}$ in the critical limit.

cond-mat↗

arXiv1997

Universal Amplitude Ratios in the 3D Ising Model

hep-lat↗

arXiv1996

String Effects in the Wilson Loop: a high precision numerical test

We test numerically the effective string description of the infrared limit of lattice gauge theories in the confining regime. We consider the 3d Z(2) lattice gauge theory, and we define ratios of Wilson loops such that the predictions of the effective string theory do not contain any adjustable parameters. In this way we are able to obtain a degree of accuracy high enough to show unambiguously that the flux--tube fluctuations are described, in the infrared limit, by an effective bosonic string theory.

hep-lat↗

arXiv1996

The Spectrum of the 2+1 Dimensional Gauge Ising Model

We present a high precision Monte Carlo study of the spectrum of the $Z_2$ gauge theory in $2+1$ dimensions in the strong coupling phase. Using state of the art Monte Carlo techniques we are able to accurately determine up to three masses in a single channel. We compare our results with the strong coupling expansion for the lightest mass and with results for the universal ratio $σ/m^2$ determined for the $ϕ^4$-theory. Finally the whole spectrum is compared with that obtained from the Isgur-Paton flux tube model and the spectrum of the $2+1$ dimensional $SU(2)$ gauge theory. A remarkable agreement between the Ising and SU(2) spectra (except for the lowest mass state) is found.

hep-lat↗

arXiv1996

Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching

We study the roughening transition of the dual of the 2D XY model, of the Discrete Gaussian model, of the Absolute Value Solid-On-Solid model and of the interface in an Ising model on a 3D simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable BCSOS model. Our estimates for the critical couplings are $β_R^{XY}=1.1199(1)$, $K_R^{DG}=0.6653(2)$ and $K_R^{ASOS}=0.80608(2)$ for the XY-model, the Discrete Gaussian model and the Absolute Value Solid-On-Solid model, respectively. For the inverse roughening temperature of the Ising interface we find $K_R^{Ising}= 0.40758(1)$. To the best of our knowledge, these are the most precise estimates for these parameters published so far.

cond-mat↗

arXiv1996

Iterating Block Spin Transformations of the O(3) Non-Linear Sigma-Model

We study the iteration of block spin transformations in the O(3) symmetric non-linear sigma-model on a two-dimensional square lattice with help of the Monte Carlo method. In contrast to the classical Monte Carlo Renormalization Group approach, we do attempt to explicitly compute the block spin effective actions. Using two different methods for the determination of effective couplings, we study the renormalization group flow for various parametrization and truncation schemes. The largest ansatz for the effective action contains thirteen coupling constants. Actions on the renormalized trajectory should describe theories with no lattice artefacts, even at small correlation length. However, tests with the step scaling function of Luescher et al. reveal that our truncated effective actions show sizable scaling violations indicating that the ansaetze are still too small.

hep-lat↗

arXiv1996

The Roughening Transition of the 3D Ising Interface: A Monte Carlo Study

We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid models. The basic idea is the matching of the renormalization-group-flow of the interface with that of the exactly solvable body centered cubic solid on solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperature $K_R=0.40754(5)$ is almost by two orders of magnitude more accurate than the estimate of Mon, Landau and Stauffer.

hep-lat↗

arXiv1995

Deconfinement transition and dimensional cross-over in the 3D gauge Ising model

We present a high precision Monte Carlo study of the finite temperature $Z_2$ gauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows us to use powerful cluster algorithms for the simulations. For temporal extensions up to $N_t=16$ we obtain the inverse critical temperature with a statistical accuracy comparable with the most accurate results for the bulk phase transition of the 3D Ising model. We discuss the predictions of T. W. Capehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions. Our precise data for the critical exponents and critical amplitudes confirm the Svetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the critical temperature of about 20%.

hep-lat↗

arXiv1995

Deconfinement, Screening and Abelian Projection at Finite Temperature

The behavior of static sources transforming according to different irreducible representations of the gauge group is studied in the context of finite temperature lattice gauge theory. We combine analytical and numerical approaches to extract information about confinement and screening both at low temperatures, and around the deconfinement phase transition. The idea that abelian projection in the Maximally Abelian Gauge reproduces the most important features of confinement and screening is tested at a quantitative level in these finite-T theories. Our results show that while this abelian projection provides correct qualitative features, it fails at a detailed quantitative level.

hep-lat↗

arXiv1995

Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$

We investigate the continuum limit in $SO(N)$ Principal Chiral Models concentrating in detail on the $SO(4)$ model and its covering group SU(2)xSU(2). We compute the mass gap in terms of Lambda_MS and compare with the prediction of Hollowood of $m/Ł_\MS = 3.8716$. We use the finite-size scaling method of Lüscher et al. to deduce $m/Ł_\MS$ and find that for the $SO(4)$ model the computed result of $m/Ł_\MS \sim 14$ is in strong disagreement with theory but that a similar analysis of the SU(2)xSU(2) yields excellent agreement with theory. We conjecture that for $SO(4)$ violations of the finite-size scaling assumption are severe forthe values of the correlation length, $ξ$, investigated and that our attempts to extrapolate the results to zero lattice spacing, although plausible, are erroneous. Conversely, the finite-size scaling violations in the SU(2)xSU(2) simulation are consistent with perturbation theory and the computed $beta-$function agrees well with the 3-loop approximation for couplings evaluated at scales $L/a \le ξ$, where $ξ$ is measured in units of the lattice spacing, $a$. We conjecture that lattice vortex artifacts in the $SO(4)$ model are responsible for delaying the onset of the continuum limit until much larger correlation lengths are achieved notwithstanding the apparent onset of scaling. Results for the mass spectrum for SO(N) m, N=8,10 are given whose comparison with theory gives plausible support to our ideas.

hep-lat↗

arXiv1994

Rough Interfaces Beyond the Gaussian Approximation

We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).

hep-lat↗

arXiv1994

Canonical Demon Monte Carlo Renormalization Group

We describe a method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. It can be used, e.g., for lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. Unlike the Microcanonical Renormalization Group of Creutz et al. it avoids systematical errors in small volumes. We present numerical results for the O(3) nonlinear sigma-model.

hep-lat↗

arXiv1994

The Sine Gordon Model: Perturbation Theory and Cluster Monte Carlo

We study the expansion of the surface thickness in the 2-dimensional lattice Sine Gordon model in powers of the fugacity z. Using the expansion to order z**2, we derive lines of constant physics in the rough phase. We describe and test a VMR cluster algorithm for the Monte Carlo simulation of the model. The algorithm shows nearly no critical slowing down. We apply the algorithm in a comparison of our perturbative results with Monte Carlo data.

hep-lat↗