Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods

Abstract

The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above and at the critical temperature. Application of the tensor-network approach is also made to the $q$-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q=3,4,5,6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.

12 pages, 14 figures. To appear in Phys. Rev. B

References in corpus (13)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Tensor renormalization group approach to 2D classical lattice models
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Observation of Lee-Yang zeros
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Phase Transition Properties of 3D Potts Models
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows
• Hard hexagon partition function for complex fugacity

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