arXiv subjects

Martin Hasenbusch

Publications and source records attributed to Martin Hasenbusch.

At least 19 recordsLinked to original sources

arXiv2025

Precision estimates of large charge RG exponents $Y_q$ in the 3D XY universality class

We accurately compute the RG exponents $Y_q$ of large $q$ fields at the $O(2)$ invariant fixed point in three dimensions. We build on an iterative approach that has been previously proposed and is implemented by using the worm algorithm. We simulate an improved XY model, that has next-to-next-to-nearest couplings in addition to nearest ones. In the worm update we incorporate weights, which allows us to obtain accurate results up to $q=64$. For example we get $Y_q=1.76370(12)$, $0.89167(23)$, and $-0.11203(34)$ for $q=2$, $3$, and $4$, respectively. The comparison with the large $q$ effective field theory gives an excellent agreement down to $q=4$ and provides accurate estimates of the parameters of the effective field theory.

hep-lat↗

arXiv2025

Monte Carlo study of the $O(2)$-invariant $\phi^4$ theory with a cubic perturbation in three dimensions

We study the $2$-component $\phi^4$ model on the simple cubic lattice in the presence of a cubic, or equivalently, a $\mathbb{D}_4$ invariant perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size scaling analysis of the data. We follow previous work on the $3$-component case. We study the RG flow from the decoupled Ising fixed point into the $O(2)$-invariant one and towards the fluctuation induced first order transition. To this end we study the behavior of phenomenological couplings. At the $O(2)$-invariant fixed point we obtain the estimate $Y_4=-0.1118(10)$ of the RG-exponent of the perturbation. Note that the small modulus of $Y_4$ means that the RG flow is slow. Hence, in order to interpret experiments or Monte Carlo simulations of lattice models, which are effectively described by the $\phi^4$ model with a cubic term, we have to consider the RG flow beyond the neighborhood of the fixed points.

cond-mat.stat-mech↗

arXiv2025

Eliminating leading and subleading corrections to scaling in the three-dimensional XY universality class

We study the $(q+1)$-state clock model on the simple cubic lattice by using Monte Carlo simulations. In addition to the nearest neighbor coupling we consider a next-to-next-to-nearest neighbor coupling. For a certain range of the parameters, the phase transition of the model shares the XY universality class. Leading corrections to scaling are studied by using finite size scaling of dimensionless quantities, such as the Binder cumulant $U_4$. The spatial unisotropy, which causes subleading corrections, is studied by computing the exponential correlation length $\xi_{exp}$ in the high temperature phase for different directions. In the case of the $q$-state clock model it turns out that by tuning the ratio of the two coupling constants, we can eliminate either leading or subleading corrections to scaling. These points on the critical line are close to each other. Hence in the improved model, where leading corrections to scaling vanish, also subleading corrections are small. By using a finite size scaling analysis of our high statistics data we obtain $\eta=0.03816(2)$ and $y_t =1/\nu=1.48872(5)$ as estimates of the critical exponents.

cond-mat.stat-mech↗

arXiv2023

$\phi^4$ lattice model with cubic symmetry in three dimensions: RG-flow and first order phase transitions

We study the $3$-component $\phi^4$ model on the simple cubic lattice in presence of a cubic perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size scaling analysis of the data. The analysis of the renormalization group (RG)-flow of a dimensionless quantity provides us with the accurate estimate $Y_4 - \omega_2 =0.00081(7)$ for the difference of the RG-eigenvalue $Y_4$ at the $O(3)$-symmetric fixed point and the correction exponent $\omega_2$ at the cubic fixed point. We determine an effective exponent $\nu_{eff}$ of the correlation length that depends on the strength of the breaking of the $O(3)$ symmetry. Field theory predicts that depending on the sign of the cubic perturbation, the RG-flow is attracted by the cubic fixed point, or runs to an ever increasing amplitude, indicating a fluctuation induced first order phase transition. We demonstrate directly the first order nature of the phase transition for a sufficiently strong breaking of the $O(3)$ symmetry. We obtain accurate results for the latent heat, the correlation length in the disordered phase at the transition temperature and the interface tension for interfaces between one of the ordered phases and the disordered phase. We study how these quantities scale with the RG-flow, allowing quantitative predictions for weaker breaking of the $O(3)$ symmetry.

hep-lat↗

arXiv2022

Cubic fixed point in three dimensions: Monte Carlo simulations of the $\phi^4$ model on the lattice

We study the cubic fixed point for $N=3$ and $4$ by using finite size scaling applied to data obtained from Monte Carlo simulations of the $N$-component $\phi^4$ model on the simple cubic lattice. We generalize the idea of improved models to a two-parameter family of models. The two-parameter space is scanned for the point, where the amplitudes of the two leading corrections to scaling vanish. To this end, a dimensionless quantity is introduced that monitors the breaking of the $O(N)$-invariance. For $N=4$, we determine the correction exponents $\omega_1=0.763(24)$ and $\omega_2=0.082(5)$. In the case of $N=3$, we obtain $Y_4=0.0142(6)$ for the RG-exponent of the cubic perturbation at the $O(3)$-invariant fixed point, while the correction exponent $\omega_2=0.0133(8)$ at the cubic fixed point. Simulations close to the improved point result in the estimates $\nu=0.7202(7)$ and $\eta=0.0371(2)$ of the critical exponents of the cubic fixed point for $N=4$. For $N=3$, at the cubic fixed point, the $O(3)$-symmetry is only mildly broken and the critical exponents differ only by little from those of the $O(3)$-invariant fixed point. We find $-0.00001 \lessapprox \eta_{cubic}- \eta_{O(3)} \lessapprox 0.00007$ and $\nu_{cubic}-\nu_{O(3)} =-0.00061(10)$.

cond-mat.stat-mech↗

arXiv2021

Three-dimensional $O(N)$-invariant $\phi^4$ models at criticality for $N\ge 4$

We study the $O(N)$-invariant $\phi^4$ model on the simple cubic lattice by using Monte Carlo simulations. By using a finite size scaling analysis, we obtain accurate estimates for the critical exponents $\nu$ and $\eta$ for $N=4$, $5$, $6$, $8$, $10$, and $12$. We study the model for each $N$ for at least three different values of the parameter $\lambda$ to control leading corrections to scaling. We compare our results with those obtained by other theoretical methods.

hep-lat↗

arXiv2021

Restoring isotropy in a three-dimensional lattice model: The Ising universality class

We study a generalized Blume-Capel model on the simple cubic lattice. In addition to the nearest neighbor coupling there is a next to next to nearest neighbor coupling. In order to quantify spatial anisotropy, we determine the correlation length in the high temperature phase of the model for three different directions. It turns out that the spatial anisotropy depends very little on the dilution parameter $D$ of the model and is essentially determined by the ratio of the nearest neighbor and the next to next to nearest neighbor coupling. This ratio is tuned such that the leading contribution to the spatial anisotropy is eliminated. Next we perform a finite size scaling (FSS) study to tune $D$ such that also the leading correction to scaling is eliminated. Based on this FSS study, we determine the critical exponents $ν=0.62998(5)$ and $η=0.036284(40)$, which are in nice agreement with the more accurate results obtained by using the conformal bootstrap method. Furthermore we provide accurate results for fixed point values of dimensionless quantities such as the Binder cumulant and for the critical couplings. These results provide the groundwork for broader studies of universal properties of the three-dimensional Ising universality class.

cond-mat.stat-mech↗

arXiv2021

Two- and three-point functions at criticality: Monte Carlo simulations of the three-dimensional $(q+1)$-state clock model

We simulate the improved $(q+1)$-state clock model on the simple cubic lattice at the critical point on lattices of a linear size up to $L=960$. We compute operator product expansion (OPE) coefficients for the three-dimensional XY universality class. These are compared with highly accurate estimates obtained by using the conformal bootstrap method. We find that the results are consistent.

cond-mat.stat-mech↗

arXiv2020

Monte Carlo study of a generalized icosahedral model on the simple cubic lattice

We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. The field variable of the icosahedral model might take one of twelve vectors of unit length, which are given by the normalized vertices of the icosahedron, as value. Similar to the Blume-Capel model, where in addition to $-1$ and $1$, as in the Ising model, the spin might take the value $0$, we add in the generalized model $(0,0,0)$ as allowed value. There is a parameter $D$ that controls the density of these voids. For a certain range of $D$, the model undergoes a second-order phase transition. On the critical line, $O(3)$ symmetry emerges. Furthermore, we demonstrate that within this range, similar to the Blume-Capel model on the simple cubic lattice, there is a value of $D$, where leading corrections to scaling vanish. We perform Monte Carlo simulations for lattices of a linear size up to $L=400$ by using a hybrid of local Metropolis and cluster updates. The motivation to study this particular model is mainly of technical nature. Less memory and CPU time are needed than for a model with $O(3)$ symmetry at the microscopic level. As the result of a finite-size scaling analysis we obtain $ν=0.71164(10)$, $η=0.03784(5)$, and $ω=0.759(2)$ for the critical exponents of the three-dimensional Heisenberg universality class. The estimate of the irrelevant renormalization group eigenvalue that is related with the breaking the $O(3)$ symmetry is $y_{ico}=-2.19(2)$.

cond-mat.stat-mech↗

arXiv2020

The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model

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.

cond-mat.stat-mech↗

arXiv2020

Monte Carlo study of an improved clock model in three dimensions

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 $η=0.03810(8)$, $ν=0.67169(7)$, and $ω=0.789(4)$. Furthermore we obtain estimates for fixed point values of phenomenological couplings and critical temperatures.

cond-mat.stat-mech↗

arXiv2018

Testing the event-chain algorithm in asymptotically free models

We apply the event-chain algorithm proposed by Bernard, Krauth and Wilson in 2009 to toy models of lattice QCD. We give a formal prove of stability of the algorithm. We study its performance at the example of the massive Gaussian model on the square and the simple cubic lattice, the $O(3)$-invariant non-linear $σ$-model and the $SU(3) \times SU(3)$ principle chiral model on the square lattice. In all these cases we find that critical slowing down is essentially eliminated.

hep-lat↗

arXiv2018

Exploiting the hopping parameter expansion in the hybrid Monte Carlo (HMC) simulation of lattice QCD with two degenerate flavours of Wilson fermions

We show how the hopping parameter expansion at order $κ^2$ and $κ^4$ can be exploited in the simulation of lattice QCD with two flavours of degenerate Wilson fermions. A natural extension of this idea is a "UV-filtering" by using rooted polynomials. These approaches can be easily combined with, for example, mass preconditioning. First numerical tests are performed for the Wilson gauge action at $β=5.6$ and $κ=0.156$ and $0.1575$.

hep-lat↗

arXiv2017

Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model

We compute two- and three-point functions at criticality for the three-dimensional Ising universality class. To this end we simulate the improved Blume-Capel model at the critical temperature on lattices of a linear size up to $L=1600$. As check also simulations of the spin-1/2 Ising model are performed. We find $f_{σσε} = 1.051(1)$ and $f_{εεε} =1.533(5)$ for operator product expansion coefficients. These results are consistent with but less precise than those recently obtained by using the bootstrap method. An important ingredient in our simulations is a variance reduced estimator of $N$-point functions. Finite size corrections vanish with $L^{-Δ_ε}$, where $L$ is the linear size of the lattice and $Δ_ε$ is the scaling dimension of the leading $Z_2$-even scalar $ε$.

hep-lat↗

arXiv2017

Fighting topological freezing in the two-dimensional CP$^{N-1}$ model

We perform Monte Carlo simulations of the CP$^{N-1}$ model on the square lattice for $N=10$, $21$, and $41$. Our focus is on the severe slowing down related to instantons. To fight this problem we employ open boundary conditions as proposed by Lüscher and Schaefer for lattice QCD. Furthermore we test the efficiency of parallel tempering of a line defect. Our results for open boundary conditions are consistent with the expectation that topological freezing is avoided, while autocorrelation times are still large. The results obtained with parallel tempering are encouraging.

hep-lat↗

arXiv2017

The interface tension in the improved Blume-Capel model

We study interfaces with periodic boundary conditions in the low temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with anti-periodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension $σ$ and the correlation length $ξ$ obtained in previous work, we determine the universal amplitude ratios $R_{2nd,+} = σ_0 f_{2nd,+}^2= 0.3863(6)$, $R_{2nd,-} = σ_0 f_{2nd,-}^2= 0.1028(1) $ and $R_{exp,-}=σ_0 f_{exp,-}^2= 0.1077(3)$. Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.

cond-mat.stat-mech↗

arXiv2017

Fighting topological freezing in the two-dimensional CP$^{N-1}$ model

We perform Monte Carlo simulations of the CP$^{N-1}$ model on the square lattice for $N=10$, $21$, and $41$. Our focus is on the severe slowing down related to instantons. To fight this problem we employ open boundary conditions as proposed by Lüscher and Schaefer for lattice QCD. Furthermore we test the efficiency of parallel tempering in a line defect. Our results for open boundary conditions are consistent with the expectation that topological freezing is avoided, while autocorrelation times are still large. The results obtained with parallel tempering are encouraging.

hep-lat↗

arXiv2015

A variance reduced estimator of the connected two-point function in the presence of a broken Z_2 symmetry

The exchange or geometric cluster algorithm allows us to define a variance reduced estimator of the connected two-point function in the presence of a broken Z_2-symmetry. We present first numerical tests for the improved Blume-Capel model on the simple cubic lattice. We perform simulations for the critical isotherm, the low temperature phase at vanishing external field and, for comparison, also the high temperature phase. For the connected two-point function a substantial reduction of the variance can be obtained, allowing us to compute the correlation length with high precision. Based on these results, estimates for various universal amplitude ratios that characterise the universality class of the three-dimensional Ising model are computed.

cond-mat.stat-mech↗