Quantum Computation of Fisher Zeros for the Ising Model

H. P. Laba, V. M. Tkachuk

Felicitas Beichert, C. Hooley, Vadim Oganesyan +1 more

Heng-Na Xiong, Xiaoguang Wang

Andrij Romanovych Kuzmak, V. M. Tkachuk

We propose a protocol for studying the purely imaginary Fisher zeros of the Ising model on a quantum computer. Our protocol is based on the direct relation between the partition function for purely imaginary temperature and the evolution operator of the Ising model. In this case, the inverse temperature is equal to the time of evolution. This protocol allows one to measure the zeros only those localized on the imaginary axes. We test this protocol on the ibm-lagos quantum computer in the cases of a 3-spin chain and a triangle cluster in a purely imaginary magnetic field, as well as a 7-spin cluster in which the interaction between spins reproduces the architecture of the quantum computer.

Simran Singh, Massimo Cipressi, Francesco Di Renzo

We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D Ising model using multipoint 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 the multipoint 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 behavior of Lee-Yang zeros. We present our finite volume scaling analysis of the zeros done at T=Tc for a few lattice sizes, extracting to a 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 βc and the critical exponent ν . Results already exist for extracting the critical exponents for the Ising model in two and three dimensions making use of Fisher and Lee-Yang zeros. In this work, multipoint Padé is shown to be competitive with this respect and thus a powerful tool to study phase transitions. Published by the American Physical Society 2024

Felicitas Beichert

In this thesis we analyse the Fisher zeros for various Ising models. We show that there is long-range spiral order on the contours of zeros for classical one-dimensional Ising chains and that there is an imaginary “latent heat” associated with crossing those contours. Then we can see how areas of Fisher zeros fill in as we turn the Ising chain into Ising ladders of different widths, which seems to contradict the standard analysis presented in the literature and can be attributed to a different approach to the thermodynamic limit. Finally, we report results on frustrated two-dimensional classical Ising lattices, in particular the triangular and the kagomé lattice, and the quantum Ising problem.