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Martin Hasenbusch - One of the best experts on this subject based on the ideXlab platform.
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dynamic critical exponent z of the three dimensional ising Universality Class monte carlo simulations of the improved blume capel model
Physical Review E, 2020Co-Authors: Martin HasenbuschAbstract:We study purely dissipative relaxational dynamics in the three-dimensional Ising Universality Class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain z=2.0245(15) for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our estimate of z is fully consistent with recent field theoretic results.
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thermodynamic casimir force a monte carlo study of the crossover between the ordinary and the normal surface Universality Class
Physical Review B, 2011Co-Authors: Martin HasenbuschAbstract:We study the crossover from the ordinary to the normal surface Universality Class in the three-dimensional Ising 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 \rightarrow \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. Maciolek, Phys. Rev. Lett. 105, 055701 (2010)], mean-field calculations and preliminary Monte Carlo simulations of the 3D Ising model, [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.
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universal amplitude ratios in the three dimensional ising Universality Class
Physical Review B, 2010Co-Authors: Martin HasenbuschAbstract:We compute a number of universal amplitude ratios in the three-dimensional Ising Universality Class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain ${A}_{+}/{A}_{\ensuremath{-}}=0.536(2)$ and ${C}_{+}/{C}_{\ensuremath{-}}=4.713(7)$, where ${A}_{\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{\ifmmode\pm\else\textpm\fi{}}$ are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts $+$ and $\ensuremath{-}$ indicate the high- and the low-temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high- and low-temperature series expansions, field theoretic methods, and experiments.
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thermodynamic casimir effect for films in the three dimensional ising Universality Class symmetry breaking boundary conditions
Physical Review B, 2010Co-Authors: Martin HasenbuschAbstract: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 +-, where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -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^-omega, where L_0 is the thickness of the film and omega approx 0.8, can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. We confirm the theoretical expectation 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 theta_++ and theta_+- 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 binary mixture.
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critical exponents and equation of state of the three dimensional heisenberg Universality Class
Physical Review B, 2002Co-Authors: Massimo Campostrini, Martin Hasenbusch, Andrea Pelissetto, Paolo Rossi, Ettore VicariAbstract: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.
Silvio C. Ferreira - One of the best experts on this subject based on the ideXlab platform.
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kardar parisi zhang Universality Class in 2 1 dimensions universal geometry dependent distributions and finite time corrections
Physical Review E, 2013Co-Authors: Tiago J. Oliveira, S. G. Alves, Silvio C. FerreiraAbstract:The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) Universality Class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as t(-β), where β is the growth exponent. Our results support a generalization of the ansatz h=v(∞)t+(Γt)(β)χ+η+ζt(-β) to higher dimensions, where v(∞), Γ, ζ, and η are nonuniversal quantities whereas β and χ are universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of the KPZ Class in two-dimensional systems.
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Eden clusters in three-dimensions and the KPZ Universality Class
arXiv: Statistical Mechanics, 2012Co-Authors: S. G. Alves, Silvio C. FerreiraAbstract:We present large-scale simulations of radial Eden clusters in three-dimensions and show that the growth exponent is in agreement with the value $\beta=0.242$ accepted for the Kardar-Parisi-Zhang (KPZ) Universality Class. Our results refute a recent assertion proposing that radial Eden growth belongs to a Universality Class distinct from KPZ. We associate the previously reported discrepancy to a slow convergence to the asymptotic limit. We also present the skewness and kurtosis in the roughening regime for flat geometry in 2+1 dimensions.
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Universal fluctuations in radial growth models belonging to the KPZ Universality Class
EPL (Europhysics Letters), 2011Co-Authors: S. G. Alves, Tiago J. Oliveira, Silvio C. FerreiraAbstract:We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ Universality Class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ Universality Class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy2 process. Our simulation results fill a lacking gap of the conjecture that had been recently verified analytically and experimentally.
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universal fluctuations in radial growth models belonging to the kpz Universality Class
arXiv: Statistical Mechanics, 2011Co-Authors: S. G. Alves, Tiago J. Oliveira, Silvio C. FerreiraAbstract:We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ Universality Class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ Universality Class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy$_2$ process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.
Tomohiro Sasamoto - One of the best experts on this subject based on the ideXlab platform.
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point interacting brownian motions in the kpz Universality Class
Electronic Journal of Probability, 2015Co-Authors: Herbert Spohn, Tomohiro SasamotoAbstract:We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives at Brownian motions with oblique reflections. For this model we prove a Bethe ansatz formula for the transition probability and self-duality. In case of half-Poisson initial data, duality is used to arrive at a Fredholm determinant for the generating function of the number of particles to the left of some reference point at any time $t > 0$. A formal asymptotics for this determinant establishes the link to the Kardar-Parisi-Zhang Universality Class.
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the 1 1 dimensional kardar parisi zhang equation and its Universality Class
Journal of Statistical Mechanics: Theory and Experiment, 2010Co-Authors: Tomohiro Sasamoto, Herbert SpohnAbstract:We explain the exact solution of the 1 + 1-dimensional Kardar–Parisi–Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ Universality Class, not only as regards scaling exponents but also as regards the full probability distribution of the height in the long time limit.
Herbert Spohn - One of the best experts on this subject based on the ideXlab platform.
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point interacting brownian motions in the kpz Universality Class
Electronic Journal of Probability, 2015Co-Authors: Herbert Spohn, Tomohiro SasamotoAbstract:We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives at Brownian motions with oblique reflections. For this model we prove a Bethe ansatz formula for the transition probability and self-duality. In case of half-Poisson initial data, duality is used to arrive at a Fredholm determinant for the generating function of the number of particles to the left of some reference point at any time $t > 0$. A formal asymptotics for this determinant establishes the link to the Kardar-Parisi-Zhang Universality Class.
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the 1 1 dimensional kardar parisi zhang equation and its Universality Class
Journal of Statistical Mechanics: Theory and Experiment, 2010Co-Authors: Tomohiro Sasamoto, Herbert SpohnAbstract:We explain the exact solution of the 1 + 1-dimensional Kardar–Parisi–Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ Universality Class, not only as regards scaling exponents but also as regards the full probability distribution of the height in the long time limit.
Helmut G. Katzgraber - One of the best experts on this subject based on the ideXlab platform.
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diluted antiferromagnets in a field seem to be in a different Universality Class than the random field ising model
Physical Review B, 2013Co-Authors: Bjoern Ahrens, Helmut G. Katzgraber, Alexander K. Hartmann, Jianping XiaoAbstract:We perform large-scale Monte Carlo simulations using the Machta-Newman-Chayes algorithms to study the critical behavior of both the diluted antiferromagnet in a field with 30% dilution and the random-field Ising model with Gaussian random fields for different field strengths. Analytical calculations by Cardy [Phys. Rev. B 29, 505 (1984)] predict that both models map onto each other and share the same Universality Class in the limit of vanishing fields. However, a detailed finite-size scaling analysis of the Binder cumulant, the two-point finite-size correlation length, and the susceptibility suggests that even in the limit of small fields, where the mapping is expected to work, both models are not in the same Universality Class. Based on our numerical data, we present analytical expressions for the phase boundaries of both models.
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Universality-Class dependence of energy distributions in spin glasses
Physical Review B, 2005Co-Authors: Helmut G. Katzgraber, Mathias Körner, Frauke Liers, Michael Jünger, Alexander K. HartmannAbstract:We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price algorithms. By tuning the exponent of the power-law interactions we are able to scan several Universality Classes. Our results suggest that mean-field models have a non-Gaussian limiting distribution of the ground-state energies, whereas non-mean-field models have a Gaussian limiting distribution. We compare the results of the disordered one-dimensional Ising chain to results for a disordered two-leg ladder, for which large system sizes can be studied, and find a qualitative agreement between the disordered one-dimensional Ising chain in the short-range Universality Class and the disordered two-leg ladder. We show that the mean and the standard deviation of the ground-state energy distributions scale with a power of the system size. In the mean-field Universality Class the skewness does not follow a power-law behavior and converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick model seem to be acceptably well fitted by a modified Gumbel distribution. Finally, we discuss the distribution of the internal energy of the Sherrington-Kirkpatrick model at finite temperatures and show that it behaves similar to the ground-state energy of the system if the temperature is smaller than the critical temperature.
