arXiv subjects

Martin Hasenbusch

Publications and source records attributed to Martin Hasenbusch.

At least 55 records · Page 3Linked to original sources

arXiv2008

Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models

We study the phase transition of thin films in the three-dimensional XY universality class. To this end, we perform a Monte Carlo study of the improved two-component ϕ^4 model, the improved dynamically diluted XY model and the standard XY model on the simple cubic lattice. We study films of a thickness up to L_0=32 lattice spacings. In the short direction of the lattice free boundary conditions are employed. Using a finite size scaling (FSS) method, proposed recently, we determine the transition temperature with high accuracy. The effectively two-dimensional finite size scaling behaviour of the Binder cumulant U_4, the second moment correlation length over the lattice size ξ_{2nd}/L, the ratio of the partition functions with anti-periodic and periodic boundary conditions Z_a/Z_p and the helicity modulus Υclearly confirm the Kosterlitz-Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L_0 of the film. The predictions of the renormalization group (RG) theory are confirmed. We compute the universal ratio of the thickness of the film L_0 and the transversal correlation length ξ_T in the three-dimensional thermodynamic limit at the Kosterlitz-Thouless transition temperature of a film of thickness L_0: [L_{0,KT}/ξ_T]^* = 1.595(7). This results can be compared with experimental results on thin films of 4He near the λ-transition.

cond-mat.stat-mech↗

arXiv2008

A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios

We simulate lattice models in the three-dimensional XY universality class in the low and the high temperature phase. This allows us to compute a number of universal amplitude ratios with unprecedented precision: R_Υ=0.411(2), R_B=2.83(1), R_ξ^+=0.3562(10) and R_ξ^-=0.850(5). These results can be compared with those obtained from other theoretical methods, such as field theoretic methods or the high temperature series expansion and also with experimental results for the lambda-transition of $^4$He. In addition to the XY model, we study the three-dimensional two-component $ϕ^4$ model on the simple cubic lattice. The parameter of the $ϕ^4$ model is chosen such that leading corrections to scaling are small.

cond-mat.stat-mech↗

arXiv2008

Critical and multicritical behavior of the +- J Ising model in two and three dimensions

We report our Monte Carlo results on the critical and multicritical behavior of the +- J Ising model [with a random-exchange probability P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p=1 to a multicritical (Nishimori) point. By a finite-size scaling analysis, we provide strong numerical evidence that in three dimensions the critical behavior along this line belongs to the same universality class as that of the critical transition in the randomly dilute Ising model. In two dimensions we confirm that the critical behavior is controlled by the pure Ising fixed point and that disorder is marginally irrelevant, giving rise to universal logarithmic corrections. In both two and three dimensions, we also determine the location of the multicritical Nishimori point, as well as the renormalization-group dimensions of the operators that control the renormalization-group flow close to it.

cond-mat.dis-nn↗

arXiv2008

The critical behavior of three-dimensional Ising spin glass models

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 ωrelated to the leading irrelevant operator: ω=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 νand η: we obtain ν=2.45(15) and η=-0.375(10).

cond-mat.dis-nn↗

arXiv2008

The Binder Cumulant at the Kosterlitz-Thouless Transition

We study the behaviour of the Binder cumulant on finite square lattices at the Kosterlitz-Thouless phase transition. We determine the fixed point value of the Binder cumulant and the coefficient of the leading logarithmic correction. These calculations are supplemented with Monte Carlo simulations of the classical XY (plane rotator) model, the Villain model and the dual of the absolute value solid-on-solid model. Using the single cluster algorithm, we simulate lattices up to L=4096. For the lattice sizes reached, subleading corrections are needed to fit the data for the Binder cumulant. We demonstrate that the combined analysis of the Binder cumulant and the second moment correlation length over the lattice size allows for an accurate determination of the Kosterlitz-Thouless transition temperature on relatively small lattices. We test the new method at the example of the 2-component phi^4 model on the lattice.

cond-mat.stat-mech↗

arXiv2008

The two dimensional XY model at the transition temperature: A high precision Monte Carlo study

We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of the second moment correlation length over the lattice size xi_{2nd}/L at the transition temperature. This new prediction and the analogous one for the helicity modulus are confronted with our Monte Carlo data. This way beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we address the puzzle of logarithmic corrections of the magnetic susceptibility chi at the transition temperature.

cond-mat.stat-mech↗

arXiv2008

Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice

We investigate the critical behavior of the random-bond +- J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the disorder parameter (p=1 corresponds to the pure Ising model). We perform a finite-size scaling analysis of high-statistics Monte Carlo simulations along the Nishimori line defined by $2p-1={\rm Tanh}(1/T)$, along which the multicritical point lies. The multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and the renormalization-group dimensions of the operators that control the multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to the thermal exponent ν= 1/y_2=4.00(3) and to the crossover exponent ϕ= y_1/y_2=2.62(6).

cond-mat.dis-nn↗

arXiv2007

HMC algorithm for two-flavour lattice QCD: Schwarz-preconditioning with a one-dimensional domain decomposition

We study a variant of the Schwarz-preconditioned HMC algorithm. In contrast to the original proposal of Lüscher, we apply the domain decomposition in one lattice direction only. This is sufficient to reduce the condition number of the fermion matrix restricted to the domains compared with the full fermion matrix. For the same linear extension of the domain, less links reside on the boundaries of the domains. Therefore it becomes e.g. practical to iterate the decomposition. We perform numerical tests for two degenerate flavours of Wilson fermions. The standard Wilson gauge action at $β=5.6$ is used. The performance of our implementation is compared with other recent studies using various types of preconditioning.

hep-lat↗

arXiv2007

The interface free energy: Comparison of accurate Monte Carlo results for the 3D Ising model with effective interface models

We provide accurate Monte Carlo results for the free energy of interfaces with periodic boundary conditions in the 3D Ising model. We study a large range of inverse temperatures, allowing to control corrections to scaling. In addition to square interfaces, we study rectangular interfaces for a large range of aspect ratios u=L_1/L_2. Our numerical results are compared with predictions of effective interface models. This comparison verifies clearly the effective Nambu-Goto model up to two-loop order. Our data also allow us to obtain the estimates T_c sigma^-1/2=1.235(2), m_0++ sigma^-1/2=3.037(16) and R_+=f_+^2 sigma_0 =0.387(2), which are more precise than previous ones.

hep-lat↗

arXiv2007

Relaxational dynamics in 3D randomly diluted Ising models

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=\infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).

cond-mat.dis-nn↗

arXiv2007

The 3D +-J Ising model at the ferromagnetic transition line

We study the critical behavior of the three-dimensional $\pm J$ Ising model [with a random-exchange probability $P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)$] at the transition line between the paramagnetic and ferromagnetic phase, which extends from $p=1$ to a multicritical (Nishimori) point at $p=p_N\approx 0.767$. By a finite-size scaling analysis of Monte Carlo simulations at various values of $p$ in the region $p_N<p<1$, we provide strong numerical evidence that the critical behavior along the ferromagnetic transition line belongs to the same universality class as the three-dimensional randomly-dilute Ising model. We obtain the results $ν=0.682(3)$ and $η=0.036(2)$ for the critical exponents, which are consistent with the estimates $ν=0.683(2)$ and $η=0.036(1)$ at the transition of randomly-dilute Ising models.

cond-mat.dis-nn↗

arXiv2007

Universality class of 3D site-diluted and bond-diluted Ising systems

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, $ν=0.683(2)$, $η=0.036(1)$, $α=-0.049(6)$, $γ=1.341(4)$, $β=0.354(1)$, $δ=4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $ω=0.33(3)$ and $ω_2=0.82(8)$.

cond-mat.dis-nn↗

arXiv2007

22nd order high-temperature expansion of nearest-neighbor models with O(2) symmetry on a simple cubic lattice

We present the high-temperature series for a nearest-neighbor model with O(2) symmetry on a simple cubic lattice with the most general single-site potential. In particular, the magnetic susceptibility and the second-moment correlation length are computed to 22nd order. The series specialized to some particular improved Hamiltonians have been already analyzed in the paper M. Campostrini, M. Hasenbusch, A. Pelissetto, and E. Vicari, Phys. Rev. B 74, 144506 (2006) [cond-mat/0605083], to determine the critical exponents and other universal quantities of the three-dimensional XY universality class.

cond-mat.stat-mech↗

arXiv2006

The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-

We simulate the improved three-dimensional two-component phi^4 model on the simple cubic lattice in the low and the high temperature phase for reduced temperatures down to |T-T_c|/T_c \approx 0.0017 on lattices of a size up to 350^3. Our new results for the internal energy and the specific heat are combined with the accurate estimates of beta_c and data for the internal energy and the specific heat at β_c recently obtained in cond-mat/0605083. We find R_α = (1-A_+/A_-)/α= 4.01(5), where alpha is the critical exponent of the specific heat and A_{\pm} is the amplitude of the specific heat in the high and the low temperature phase, respectively.

cond-mat.stat-mech↗

arXiv2006

The critical exponents of the superfluid transition in He4

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class, which apply to the superfluid transition in He4 along the lambda-line of its phase diagram. We obtain the estimates alpha=-0.0151(3), nu=0.6717(1), eta=0.0381(2), gamma=1.3178(2), beta=0.3486(1), and 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 alpha disagrees with the most recent experimental estimate alpha=-0.0127(3) at the superfluid transition of He4 in microgravity environment.

cond-mat.stat-mech↗

arXiv2006

High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model

Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation.

hep-lat↗

arXiv2005

On the effective string spectrum of the tridimensional Z(2) gauge model

We study the Z(2) lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop correlation function, which is measured in the 3d Ising spin system using duality. This allows us to perform a stringent comparison with the predictions of effective string models. We find a remarkable agreement between the numerical estimates and the Nambu-Goto predictions for the energy gaps at intermediate and large distances. The precision of our data allows to distinguish clearly between the predictions of the full Nambu-Goto action and the simple free string model up to an interquark distance $r \approx 10/\sqrtσ$. At the same time, our results also confirm the breakdown of the effective picture at short distances, supporting the hypothesis that terms which are not taken into account in the usual Nambu-Goto string formulation yield a non-trivial shift to the energy levels. Furthermore, we discuss the theoretical implications of these results.

hep-lat↗

arXiv2005

Multicritical behavior in the fully frustrated XY model and related systems

We study the phase diagram and critical behavior 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 square lattices L x L, 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 behavior at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behavior 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 behavior of the 4-vector model.

cond-mat.stat-mech↗