Exploring Lee-Yang and Fisher Zeros in the 2D Ising Model through Multi-Point Padé Approximants
arxiv(2023)
摘要
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 very good precision the (combination of)
critical exponents βδ. The computation at the critical temperature
is performed after the latter has been determined via the study of Fisher
zeros, thus extracting both β_c and the critical exponent ν. 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.
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