PD Dr. Martin Hasenbusch
Profil
Forschungsthemen4
Algorithms for lattice QCD and related models
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 10/2016 - 09/2018 Projektleitung: PD Dr. Martin Hasenbusch, Prof. Dr. rer. nat. Peter Uwer
Kritische Casimirkraft zwischen Kugel und Ebenen: Monte-Carlo-Simulation von Spinmodellen
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 10/2013 - 09/2015 Projektleitung: PD Dr. Martin Hasenbusch
Kritischer Casimireffekt: Monte-Carlo-Simulationen verbesserter Modelle
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 11/2008 - 10/2010 Projektleitung: PD Dr. Martin Hasenbusch
Kritischer Casimireffekt: Monte-Carlo-Simulationen verbesserter Modelle II
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 01/2011 - 12/2012 Projektleitung: PD Dr. Martin Hasenbusch
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Publikationen25
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Physical review. B, Condensed matter · 479 Zitationen · DOI
We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find $\ensuremath{\gamma}=1.3960(9),$ $\ensuremath{\nu}=0.7112(5),$ $\ensuremath{\eta}=0.0375(5),$ $\ensuremath{\alpha}=\ensuremath{-}0.1336(15),$ $\ensuremath{\beta}=0.3689(3),$ and $\ensuremath{\delta}=4.783(3).$ We consider an improved lattice ${\ensuremath{\varphi}}^{4}$ Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the ${\ensuremath{\varphi}}^{4}$ improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.
Physical review. B, Condensed matter · 379 Zitationen · DOI
We improve the theoretical estimates of the critical exponents for the three-dimensional $\mathrm{XY}$ universality class. We find $\ensuremath{\alpha}=\ensuremath{-}0.0146(8),$ $\ensuremath{\gamma}=1.3177(5),$ $\ensuremath{\nu}=0.67155(27),$ $\ensuremath{\eta}=0.0380(4),$ $\ensuremath{\beta}=0.3485(2),$ and $\ensuremath{\delta}=4.780(2).$ We observe a discrepancy with the most recent experimental estimate of $\ensuremath{\alpha};$ this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.
Physical Review B · 326 Zitationen · DOI
We study the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter $D$ on the simple cubic lattice. To this end we perform Monte Carlo simulations using a hybrid of the local Metropolis, the single cluster and the wall cluster algorithm. Using finite size scaling we determine the value ${D}^{\ensuremath{\ast}}=0.656(20)$ of the parameter $D$, where leading corrections to scaling vanish. We find $\ensuremath{\omega}=0.832(6)$ for the exponent of leading corrections to scaling. In order to compute accurate estimates of critical exponents, we construct improved observables that have a small amplitude of the leading correction for any model. Analyzing data obtained for $D=0.641$ and 0.655 on lattices of a linear size up to $L=360$ we obtain $\ensuremath{\nu}=0.63002(10)$ and $\ensuremath{\eta}=0.03627(10)$. We compare our results with those obtained from previous Monte Carlo simulations and high-temperature series expansions of lattice models, by using field-theoretic methods and experiments.
Physics Letters B · 325 Zitationen · DOI
We propose a modification of the hybrid Monte Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is that the pseudo-fermion action is split into two parts. We test our proposal at the example of the two-dimensional lattice Schwinger model with two degenerate flavours of Wilson-fermions.
Physical Review B · 265 Zitationen · DOI
We improve the theoretical estimates of the critical exponents for the three-dimensional $XY$ universality class that apply to the superfluid transition in $^{4}\mathrm{He}$ along the $\ensuremath{\lambda}$ line of its phase diagram. We obtain the estimates $\ensuremath{\alpha}=\ensuremath{-}0.0151(3)$, $\ensuremath{\nu}=0.6717(1)$, $\ensuremath{\eta}=0.0381(2)$, $\ensuremath{\gamma}=1.3178(2)$, $\ensuremath{\beta}=0.3486(1)$, and $\ensuremath{\delta}=4.780(1)$. Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size $L=128$ and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent $\ensuremath{\alpha}$ disagrees with the most recent experimental estimate $\ensuremath{\alpha}=\ensuremath{-}0.0127(3)$ at the superfluid transition of $^{4}\mathrm{He}$ in a microgravity environment.
Nuclear Physics B · 144 Zitationen · DOI
Physical review. B, Condensed matter · 139 Zitationen · DOI
We compute an improved action for the Ising universality class in three dimensions that has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the $\ifmmode\pm\else\textpm\fi{}1$ Ising model with nearest-neighbor and body diagonal interaction, the spin-1 model with states $0,\ifmmode\pm\else\textpm\fi{}1$, and nearest-neighbor interaction, and ${\ensuremath{\varphi}}^{4}$ theory on the lattice (Landau-Ginzburg model). The remarkable finite-size scaling properties of the suitably tuned spin-1 model are compared in detail with those of the standard Ising model. Great care is taken to estimate the systematic errors from residual corrections to scaling. Our best estimates for the critical exponents are $\ensuremath{\nu}=0.6298(5)$ and $\ensuremath{\eta}=0.0366(8)$, where the given error estimates take into account the statistical and systematic uncertainties.
Physical Review B · 133 Zitationen · DOI
We investigate the effects of anisotropic perturbations in three-dimensional O($N$)-symmetric vector models. In order to assess their relevance for the critical behavior, we determine the renormalization-group dimensions of the anisotropic perturbations associated with the first few spin values of the representations of the O($N$) group, because the lowest spin values give rise to the most important effects. In particular, we determine them up to spin 4 for $N=2,\phantom{\rule{0.222222em}{0ex}}3,\phantom{\rule{0.222222em}{0ex}}4$, by finite-size analyses of Monte Carlo simulations of lattice O($N$) models, achieving a significant improvement of their accuracy. These results are relevant for several physical systems, such as density-wave systems, magnets with cubic symmetry, and multicritical phenomena arising from the competition of different order parameters.
Journal of Physics A Mathematical and General · 131 Zitationen · DOI
We study corrections to scaling in the O(3)and O(4)-symmetric 4 model on the three-dimensional simple cubic lattice with nearest neighbour interactions. For this purpose, we use Monte Carlo simulations in connection with a finite size scaling method. We find that there exists a finite value of the coupling * , for both values of N , where leading corrections to scaling vanish. As a first application, we compute the critical exponents = 0.710(2) and = 0.0380(10) for N = 3 and = 0.749(2) and = 0.0365(10) for N = 4.
Physical Review B · 116 Zitationen · DOI
We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size L: the +/- J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to L=28 and L=20, respectively), and the bond-diluted bimodal model for bond-occupation probability p(b)=0.45 (up to L=16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent omega related to the leading irrelevant operator: omega=1.0(1). Shorter Monte Carlo simulations of the bond-diluted bimodal models at p(b)=0.7 and p(b)=0.35 (up to L=10) and of the Ising spin glass model with Gaussian bond distribution (up to L=8) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain nu=2.45(15) and eta=-0.375(10).
Physica A Statistical Mechanics and its Applications · 111 Zitationen · DOI
Physical review. B./Physical review. B · 109 Zitationen · DOI
We study a generalized clock model on the simple cubic lattice. The parameter of the model can be tuned such that the amplitude of the leading correction to scaling vanishes. In the main part of the study, we simulate the model with ${Z}_{8}$ symmetry. At the transition, with increasing length scale, $O(2)$ symmetry emerges. We perform Monte Carlo simulations using a hybrid of local Metropolis and cluster algorithms of lattices with a linear size up to $L=512$. The field variable requires less memory and the updates are faster than for a model with $O(2)$ symmetry at the microscopic level. Our finite-size scaling analysis yields accurate estimates for the critical exponents of the three-dimensional $XY$-universality class. In particular, we get $\ensuremath{\eta}=0.03810(8),\ensuremath{\nu}=0.67169(7)$, and $\ensuremath{\omega}=0.789(4)$. Furthermore, we obtain estimates for fixed point values of phenomenological couplings and critical temperatures.
Journal of Physics A Mathematical and General · 96 Zitationen · DOI
We present a Monte Carlo study of the one-component $\phi^4$ model on the cubic lattice in three dimensions. Leading order scaling corrections are studied using the finite size scaling method. We compute the corrections to scaling exponent $\omega$ with high precision. We determine the value of the coupling $\lambda$ at which leading order corrections to scaling vanish. Using this result we obtain estimates for critical exponents that are more precise than those obtained with field theoretic methods.
Journal of Statistical Mechanics Theory and Experiment · 93 Zitationen · DOI
We study the phase diagram and critical behaviour of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on L x L square lattices, up to L = O(10(3)). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range order. The FFXY model and the other models, in a rather large parameter region, show a crossover behaviour at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behaviour is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero-temperature transition. A possible candidate is the O(4) point that controls the low-temperature behaviour of the 4-vector model.
Physica A Statistical Mechanics and its Applications · 92 Zitationen · DOI
Journal of Physics A Mathematical and General · 88 Zitationen · DOI
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 βXY R = 1.1199(1), KDG R = 0.6653(2) and KASOS R = 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 Ising R = 0.40758(1). To the best of our knowledge, these are the most precise estimates for these parameters published so far. 1
International Journal of Modern Physics C · 81 Zitationen · DOI
We review Monte Carlo simulations of the Ising model and similar models in three dimensions that were performed in the last decade. Only recently, Monte Carlo simulations provide more accurate results for critical exponents than field theoretic methods, such as the ∊-expansion. These results were obtained with finite size scaling and "improved actions". In addition, we summarize Monte Carlo results for universal amplitude ratios, the interface tension, and the dimensional crossover from three to two dimensions.
Physics Letters B · 81 Zitationen · DOI
Journal of Physics A Mathematical and General · 73 Zitationen · DOI
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 $\phi^4$ theory and high and low temperature series expansions of the Ising model. The mismatch with a previous Montecarlo study by Ruge et al. remains to be understood.
Physics Letters B · 72 Zitationen · DOI
Physical Review B · 65 Zitationen · DOI
We study the crossover from the ordinary to the normal surface universality class in the three-dimensional Ising bulk universality class. This crossover is relevant for the behavior of films of binary mixtures near the demixing point and a weak adsorption at one or both surfaces. We perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. We consider systems with film geometry, where various boundary conditions are applied. We discuss corrections to scaling that are caused by the surfaces and their relation with the so called extrapolation length. To this end, we analyze the behavior of the magnetization profile near the surfaces of films. We obtain an accurate estimate of the renormalization-group exponent ${y}_{{h}_{1}}=0.7249(6)$ for the ordinary surface universality class. Next we study the thermodynamic Casimir force in the crossover region from the ordinary to the normal surface universality class. To this end, we compute the Taylor expansion of the crossover finite-size scaling function up to the second order in ${h}_{1}$ around ${h}_{1}=0$, where ${h}_{1}$ is the external field at one of the surfaces. We check the range of applicability of the Taylor expansion by simulating at finite values of ${h}_{1}$. Finally, we study the approach to the strong adsorption limit ${h}_{1}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our results confirm the qualitative picture that emerges from exact calculations for stripes of the two-dimensional Ising model [D. B. Abraham and A. Macio\l{}ek, Phys. Rev. Lett. 105, 055701 (2010)], mean-field calculations, and preliminary Monte Carlo simulations of the Ising model on the simple cubic lattice [T. F. Mohry et al., Phys. Rev. E 81, 061117 (2010)]: For certain choices of ${h}_{1}$ and the thickness of the film, the thermodynamic Casimir force changes sign as a function of the temperature, and for certain choices of the temperature and ${h}_{1}$, it also changes sign as a function of the thickness of the film.
Physical Review B · 63 Zitationen · DOI
We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry-breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases $++$, where all spins at the boundary are fixed to $+1$ and $+\ensuremath{-}$, where the spins at one boundary are fixed to $+1$ while those at the other boundary are fixed to $\ensuremath{-}1$. An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to ${L}_{0}^{\ensuremath{-}\ensuremath{\omega}}$, where ${L}_{0}$ is the thickness of the film and $\ensuremath{\omega}\ensuremath{\approx}0.8$, can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. The analysis of our data shows that these corrections can be accounted for by an effective thickness ${L}_{0,eff}={L}_{0}+{L}_{s}$. Studying the correlation length of the films, the energy per area, the magnetization profile, and the thermodynamic Casimir force at the bulk critical point we find ${L}_{s}=1.9(1)$ for our model and the boundary conditions discussed here. Using this result for ${L}_{s}$ we find a nice collapse of the finite-size scaling curves obtained for the thicknesses ${L}_{0}=8.5$, 16.5, and 32.5 for the full range of temperatures that we consider. We compare our results for the finite-size scaling functions ${\ensuremath{\theta}}_{++}$ and ${\ensuremath{\theta}}_{+\ensuremath{-}}$ of the thermodynamic Casimir force with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher local-functional method, field theoretic methods, and an experiment with a classical binary liquid mixture.
Journal of Statistical Mechanics Theory and Experiment · 63 Zitationen · DOI
We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, ν = 0.680(2), η = 0.036(1), α = −0.040(6), γ = 1.335(4), β = 0.352(1), δ = 4.792(6), and of the leading and next-to-leading correction-to-scaling exponents, ω = 0.33(3) and ω2 = 0.82(8).Universality class of 3D site-diluted and bond-diluted Ising systems 2 1.
Physica A Statistical Mechanics and its Applications · 60 Zitationen · DOI
Nuclear Physics B · 59 Zitationen · DOI
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Stammdaten
Identität, Organisation und Kontakt aus HU-FIS.
- Name
- PD Dr. Martin Hasenbusch
- Titel
- PD Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Physik
- Arbeitsgruppe
- Theoretische Physik (Phänomenologie der Elementarteilchenphysik jenseits des Standardmodells)
- Telefon
- +49 30 2093-7646
- HU-FIS-Profil
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