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

TL;DR

This paper investigates finite-size effects on the microcanonical temperature in entropic sampling, proposing an analytic expression and validating it across different lattice models with phase transitions.

Contribution

It introduces an analytic expression for finite-size effects on the microcanonical temperature and validates it with exact and numerical results across multiple models.

Findings

Finite slopes are due to finite-size effects.

The proposed $a\,\ln(bL)$ expression fits data well.

Parameters $a$ and $b$ are consistent across models.

Abstract

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.