Finite-size scaling considerations on the ground state microcanonical temperature in entropic sampling simulations

In this work we discuss the behavior of the microcanonical temperature $\frac{\partial S(E)}{\partial E}$ obtained by means of numerical entropic sampling studies. It is observed that in almost all cases the slope of the logarithm of the density of states $S(E)$ is not infinite in the ground state, since as expected it should be directly related to the inverse temperature $\frac{1}{T}$. Here we show that these finite slopes are in fact due to finite-size effects and we propose an analytic expression $a\ln(bL)$ for the behavior of $\frac{\varDelta S}{\varDelta E}$ when $L\rightarrow\infty$. To test this idea we use three distinct two-dimensional square lattice models presenting second-order phase transitions. We calculated by exact means the parameters $a$ and $b$ for the two-states Ising model and for the $q=3$ and $4$ states Potts model and compared with the results obtained by entropic sampling simulations. We found an excellent agreement between exact and numerical values. We argue that this new set of parameters $a$ and $b$ represents an interesting novel issue of investigation in entropic sampling studies for different models

Wang-Landau sampling in three-dimensional polymers

Monte Carlo simulations using Wang-Landau sampling are performed to study three-dimensional chains of homopolymers on a lattice. We confirm the accuracy of the method by calculating the thermodynamic properties of this system. Our results are in good agreement with those obtained using Metropolis importance sampling. This algorithm enables one to accurately simulate the usually hardly accessible low-temperature regions since it determines the density of states in a single simulation.Comment: 5 pages, 9 figures arch-ive/Brazilian Journal of Physic

Short-time behavior of a classical ferromagnet with double-exchange interaction

We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with double-exchange interaction. Estimates for the dynamic critical exponents $z$ and $\theta$ are obtained using short-time Monte Carlo simulations. We also estimate the static critical exponents $\nu$ and $\beta$ studying the behavior of the samples at an early time. Our results are in good agreement with available estimates and support the assertion that this model and the classical Heisenberg model belong to the same universality class

Wang-Landau sampling: Improving accuracy

In this work we investigate the behavior of the microcanonical and canonical averages of the two-dimensional Ising model during the Wang-Landau simulation. The simulations were carried out using conventional Wang-Landau sampling and the $1/t$ scheme. Our findings reveal that the microcanonical average should not be accumulated during the initial modification factors \textit{f} and outline a criterion to define this limit. We show that updating the density of states only after every $L^2$ spin-flip trials leads to a much better precision. We present a mechanism to determine for the given model up to what final modification factor the simulations should be carried out. Altogether these small adjustments lead to an improved procedure for simulations with much more reliable results. We compare our results with $1/t$ simulations. We also present an application of the procedure to a self-avoiding homopolymer

The Rubber Band Revisited: Wang-Landau Simulation

In this work we apply Wang-Landau simulations to a simple model which has exact solutions both in the microcanonical and canonical formalisms. The simulations were carried out by using an updated version of the Wang-Landau sampling. We consider a homopolymer chain consisting of $N$ monomers units which may assume any configuration on the two-dimensional lattice. By imposing constraints to the moves of the polymers we obtain three different models. Our results show that updating the density of states only after every $N$ monomers moves leads to a better precision. We obtain the specific heat and the end-to-end distance per monomer and test the precision of our simulations comparing the location of the maximum of the specific heat with the exact results for the three types of walks