Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling
137
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+epsilon$ dimensions. We found that the long length scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $sigma$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at T=0, therefore the uncertainty in the phase diagram of this model is removed.
rate research
Read More
Corrections to scaling in the 3D Ising model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (gamma-1)/nu (approximately 0.38), the leading correction-to-scaling exponent being omega =< (gamma-1)/nu. A numerical estimation of omega from the susceptibility data within 40 =< L =< 2048 yields omega=0.25(33). It is consistent with the statement omega =< (gamma-1)/nu, as well as with the value omega = 1/8 of the GFD theory. We reconsider the MC estimation of omega from smaller lattice sizes to show that it does not lead to conclusive results, since the obtained values of omega depend on the particular method chosen. In particular, estimates ranging from omega =1.274(72) to omega=0.18(37) are obtained by four different finite-size scaling methods, using MC data for thermodynamic average quantities, as well as for partition function zeros. We discuss the influence of omega on the estimation of exponents eta and nu.
The Quantum Monte Carlo method for spin 1/2 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy and chemical potential as a function of temperature. We give upper bounds on the critical temperature T_c for the onset of superfluidity, obtained by studying the finite size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range -0.5 le (k_F a)^{-1} le 0.2, where a is the s-wave scattering length and k_F is the Fermi momentum of a non-interacting gas at the same density. In all cases our data is consistent with normal Fermi gas behavior above a characteristic temperature T_0 > T_c, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For T_c < T < T_0 we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low temperature results for the energy and the pairing gap are shown and compared with Green Function Monte Carlo results by other groups.
By using a simulated annealing approach, Monte Carlo and molecular-dynamics techniques we have studied static and dynamic behavior of the classical two-dimensional anisotropic Heisenberg model. We have obtained numerically that the vortex developed in such a model exhibit two different behaviors depending if the value of the anisotropy $lambda$ lies below or above a critical value $lambda_c$ . The in-plane and out-of-plane correlation functions ($S^{xx}$ and $S^{zz}$) were obtained numerically for $lambda < lambda_c$ and $lambda > lambda_c$ . We found that the out-of-plane dynamical correlation function exhibits a central peak for $lambda > lambda_c$ but not for $lambda < lambda_c$ at temperatures above $T_{BKT}$ .
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.
We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $xi_parallel$ in the direction along defects, and a perpendicular correlation length $xi_perp$ in the direction perpendicular to the lines. Both $xi_parallel$ and $xi_perp$ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents $ u_parallel$ and $ u_perp$ take different values. This property is specific for anisotropic scaling and the ratio $ u_parallel/ u_perp$ defines the anisotropy exponent $theta$. Estimates of quantitative characteristics of the critical behaviour for such systems were only obtained up to now within the renormalization group approach. We report a study of the anisotropic scaling in this system via Monte Carlo simulation of the three-dimensional system with Ising spins and non-magnetic impurities arranged into randomly distributed parallel lines. Several independent estimates for the anisotropy exponent $theta$ of the system are obtained, as well as an estimate of the susceptibility exponent $gamma$. Our results corroborate the renormalization group predictions obtained earlier.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
