arXiv subjects

Álvaro de Almeida Caparica

Publications and source records attributed to Álvaro de Almeida Caparica.

2 recordsLinked to original sources

arXiv2015

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.

cond-mat.stat-mech↗

arXiv2015

Wang-Landau sampling: a criterion for halting the simulations

In this work we propose a criterion to finish the simulations of the Wang-Landau sampling. Instead of determining a final modification factor for all simulations and every sample sizes, we investigate the behavior of the temperature of the peak of the specific heat during the simulations and finish them when this value varies bellow a given limit. As a result, different runs stop at different final modification factors. We show that in place of the temperature of the peak of the specific heat one can adopt alternatively the integrated heat transfer as a reference quantity. We apply this technique to the two-dimensional Ising model and a homopolymer. We verify that for the Ising model the mean order of the final modification factors are roughly the same for all lattice sizes, but for the homopolymer the order of the final modification factors increases with increasing polymer sizes. The results show that the simulations can be halted much earlier then it is conventional in Wang-Landau sampling, but manifold finite-size simulations are required in order to obtain accurate results. A brief application to the three-dimensional Ising model is also available.

cond-mat.stat-mech↗