Finding the dominant zero of the energy probability distribution

Abstract

In this work, we present a computational procedure to locate the dominant Fisher zero of the partition function of a thermodynamic system. The procedure greatly reduces the required computer processing time to find the dominant zero when compared to other dominant zero search procedures. As a consequence, when the partition function results in very large polynomials, the accuracy of the results can be increased, since less drastic truncation of the polynomials (or even no truncation) is necessary. We apply the procedure to the 2D Ising model in a square lattice, obtaining very accurate results for the critical temperature and some of the critical exponents of the model. We also show the results obtained when the technique is used with the Monte Carlo simulated 2D Ising model in large lattices.

Connecting the unstable region of the entropy to the pattern of the Fisher zeros map

“…The first part, Z < , includes energies E < E ′ , Z ′ covers the energy range of the non-stable region [E ′ , E ′′ ] (as discussed in section 2.1), and Z> accounts for energies E > E ′ ′ . It can be claimed that Z ′ (B = B j ) ≈ 0 since approaches that truncate the energy range, such as the zeros of the DOS [15][16][17], can capture the indications of phase transitions. Thus, we have:…”