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Partition Function Zeros of the Frustrated - Ising Model on the Honeycomb Lattice.
Entropy (Basel)
October 2024
Institut für Theoretische Physik, Leipzig University, IPF 231101, 04081 Leipzig, Germany.
We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor (J1>0) and next-nearest-neighbor (J2<0) interactions on the honeycomb lattice. We consider the finite-size scaling (FSS) of the leading Fisher and Lee-Yang zeros as determined from a cumulant method and compare it to a traditional scaling analysis based on the logarithmic derivative of the magnetization ∂ln⟨|M|⟩/∂β and the magnetic susceptibility χ. While for this model both FSS approaches are subject to strong corrections to scaling induced by the frustration, their behavior is rather different, in particular as the ratio R=J2/J1 is varied.
View Article and Find Full Text PDFYang-Lee zeros of certain antiferromagnetic models.
Phys Rev E
July 2024
Physics Department, University of California, Santa Cruz, California 95064, USA.
We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice and the more tractable mean-field model corresponding to infinite-ranged coupling between all sites. In the high-temperature limit, we show that the logarithm of the Yang-Lee zeros can be written as a series in half odd integer powers of the inverse temperature, k, with the leading term ∼k^{1/2}.
View Article and Find Full Text PDFYang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity.
Phys Rev Lett
November 2023
Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan.
Yang and Lee investigated phase transitions in terms of zeros of partition functions, namely, Yang-Lee zeros [Phys. Rev. 87, 404 (1952)PHRVAO0031-899X10.
View Article and Find Full Text PDFTwo-dimensional dilute Baxter-Wu model: Transition order and universality.
Phys Rev E
August 2023
Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.
We investigate the critical behavior of the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal-field coupling Δ with the goal of determining the universality class of transitions along the second-order part of the transition line as one approaches the putative location of the multicritical point. We employ extensive Monte Carlo simulations using two different methodologies: (i) a study of the zeros of the energy probability distribution, closely related to the Fisher zeros of the partition function, and (ii) the well-established multicanonical approach employed to study the probability distribution of the crystal-field energy. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram supports previous claims that the transition belongs to the universality class of the four-state Potts model.
View Article and Find Full Text PDFProposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays.
Phys Rev Lett
August 2023
Department of Physics, National University of Singapore, Singapore 117551, Singapore.
Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding nonunitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models.
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