Related papers: Logarithmic Corrections in the 2D XY Model
We test an improved finite-size scaling method for reliably extracting the critical temperature $T_{\rm BKT}$ of a Berezinskii-Kosterlitz-Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness…
The measurements of the magnetic and nematic correlation lengths in a generalization of the two dimensional XY model on the square lattice are presented using classical Monte Carlo simulation. The full phase diagram is re-examined based on…
The critical behaviour of statistical models with long-range interactions exhibits distinct regimes as a function of $\rho$, the power of the interaction strength decay. For $\rho$ large enough, $\rho>\rho_{\rm sr}$, the critical behaviour…
We present a Monte Carlo study of the two-component $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics…
Earlier Monte-Carlo calculations on the dissipative two-dimensional XY model are extended in several directions. We study the phase diagram and the correlation functions when dissipation is very small, where it has properties of the…
We present a dynamic Monte Carlo study of the Kosterlitz-Thouless phase transition for the spin-1/2 quantum XY model in two dimensions. The short-time dynamic scaling behaviour is found and the dynamical exponent $\theta$, $z$ and the…
In recent years, static and dynamic properties of non-$180^\circ$ domain walls in magnetic materials have attracted a great deal of interest. In this paper, spin-reorientation critical dynamics in the two-dimensional XY model is…
We have studied the superfluid density and the specific heat of the XY model on lattices L x L x H with L >> H (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method. In the H-direction we applied staggered…
While the 3d Ising model has defied analytic solution, various numerical methods like Monte Carlo, MCRG and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff…
We use finite--size scaling of Lee--Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn $O(2)$ model. We present evidence that, like the closely related $XY$--model, this has a phase transition…
Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the…
Monte Carlo results for the moments <M^k> of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary…
A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the…
We consider the 2D $J_1-J_2$ classical XY model on a square lattice. In the frustrated phase corresponding to $J_2>J_1/2$, an Ising like order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete $Z_2$ symmetry…
Based on the short-time dynamic scaling form, a novel dynamic approach is proposed to tackle numerically the Kosterlitz-Thouless phase transition. Taking the two-dimensional XY model as an example, the exponential divergence of the spatial…
We present detailed Monte Carlo results for a two-dimensional grain boundary model on a lattice. The effective Hamiltonian of the system results from the microscopic interaction of grains with orientations described by spins of unit length,…
We investigate the finite-size-scaling (FSS) behavior of the leading Fisher zero of the partition function in the complex temperature plane in the $p$-state clock models of $p=5$ and $6$. We derive the logarithmic finite-size corrections to…
A numerical study of the neutral two-dimensional (2D) lattice Coulomb gas is performed to examine dynamic scaling, finite size effects, and the dynamic critical exponent $z$ of the Kosterlitz-Thouless-Berezinskii transition. By studying…
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize…
With large-scale Monte Carlo simulations, we confirm that for the two-dimensional XY model, there is a logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered state, while only an inverse power law…