Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions
107
0
0.0
(
0
)
Added by
Luisberis Velazquez-Abad
Publication date
2013
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Recently, Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms based on canonical ensemble, which is aimed to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions. We show in this work that Monte Carlo algorithms extended with this methodology also exhibit a remarkable efficiency near a critical point. Our study is performed for the particular case of 2D four-state Potts model on the square lattice with periodic boundary conditions. This analysis reveals that the extended version of Metropolis importance sample is more efficient than the usual Swendsen-Wang and Wolff cluster algorithms. These results demonstrate the effectiveness of this methodology to improve the efficiency of MC simulations of systems that undergo any type of temperature-driven phase transition.
rate research
Read More
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.
We propose an efficient procedure for determining phase diagrams of systems that are described by spin models. It consists of combining cluster algorithms with the method proposed by Sauerwein and de Oliveira where the grand canonical potential is obtained directly from the Monte Carlo simulation, without the necessity of performing numerical integrations. The cluster algorithm presented in this paper eliminates metastability in first order phase transitions allowing us to locate precisely the first-order transitions lines. We also produce a different technique for calculating the thermodynamic limit of quantities such as the magnetization whose infinite volume limit is not straightforward in first order phase transitions. As an application, we study the Andelman model for Langmuir monolayers made of chiral molecules that is equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the phase diagrams in the case where the intermolecular forces favor interactions between enantiomers of the same type (homochiral interactions). In particular, we have determined diagrams in the surface pressure versus concentration plane which are more relevant from the experimental point of view and less usual in numerical studies.
The unconstrained ensemble describes completely open systems whose control parameters are chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up a new avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.
We use Monte Carlo simulations to study ${rm Ni Fe_2O_4}$ nanoparticles. Finite size and surface effects differentiate them from their bulk counterparts. A continuous version of the Wang-Landau algorithm is used to calculate the joint density of states $g(M_z, E)$ efficiently. From $g(M_z, E)$, we obtain the Bragg-Williams free energy of the particle, and other physical quantities. The hysteresis is observed when the nanoparticles have both surface disorder and surface anisotropy. We found that the finite coercivity is the result of interplay between surface disorder and surface anisotropy. If the surface disorder is absent or the surface anisotropy is relatively weak, the nanoparticles often exhibit superparamagnetism.
We show how the directed-loop Monte Carlo algorithm can be applied to study vertex models. The algorithm is employed to calculate the arrow polarization in the six-vertex model with the domain wall boundary conditions (DWBC). The model exhibits spatially separated ordered and ``disordered regions. We show how the boundary between these regions depends on parameters of the model. We give some predictions on the behavior of the polarization in the thermodynamic limit and discuss the relation to the Arctic Circle theorem.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
