Exploring Lee-Yang and Fisher Zeros in the 2D Ising model through multipoint Padé approximants

Abstract

We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D Ising model using multi-point Padé approximants. We perform simulations for the 2D Ising model with ferromagnetic couplings both in the absence and in the presence of a magnetic field using a cluster spin-flip algorithm. We show that it is possible to extract genuine signature of Lee Yang and Fisher zeros of the theory through the poles of magnetization and specific heat, using multi-point Padé method. We extract the poles of magnetization using Padé approximants and compare their scaling with known results. We verify the circle theorem associated to the well known behaviour of Lee Yang zeros. We present our finite volume scaling analysis of the zeros done at $T=T_c$ for a few lattice sizes, extracting to a good precision the (combination of) critical exponents $\beta \delta$. The computation at the critical temperature is performed after the latter has been determined via the study of Fisher zeros, thus extracting both ${\beta }_c$ and the critical exponent $\nu$. Results already exist for extracting the critical exponents for the Ising model in 2 and 3 dimensions making use of Fisher and Lee Yang zeros. In this work, multi-point Padé is shown to be competitive with this respect and thus a powerful tool to study phase transitions.

arXiv comment13 pages, 10 figures and 1 table, Fig. 6 and Table 1 updated. Matches accepted version

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Cited by in corpus (4)

• Locating Critical Points Using Ratios of Lee-Yang Zeros
• Lee-Yang-zero ratio method in three-dimensional Ising model
• Padé Approximation and Partition Function Zeros
• Detecting the purely imaginary Fisher zeros of an Ising spin system on a quantum computer