Work

Free-fermion approach to the partition function zeros: Special boundary conditions and product form of solution

Year: 2025

Type: article

Abstract: Partition function zeros are powerful tools in understanding critical behavior. In this paper, we present results of the Fisher zeros of two-dimensional Ising models, in the framework of free-fermion eight-vertex model. First, we succeed in finding special boundary conditions for the free-fermion model, under which the partition function of a finite lattice can be expressed in a double product form. Using appropriate mappings, these boundary conditions are transformed into the corresponding versions of the square, triangular, and honeycomb lattice Ising models. Each Ising model is studied in the cases of a zero field and of an imaginary field i ( π / 2 ) k B T . For the square lattice model, we rediscover the famous Brascamp-Kunz (B-K) boundary conditions. For the triangular and honeycomb lattice models, we obtain the B-K-type boundary conditions, and the Fisher zeros are conveniently solved from the product form of partition function. The advantage of B-K-type boundary conditions is that the Fisher zeros of any finite lattice exactly lie on certain loci, and the accumulation points of zeros can be easily determined in the thermodynamic limit. Our finding and method would be very helpful in studying the partition function zeros of vertex and Ising models.

Source: Physical Review Research

DOI: 10.1103/b6d1-6sk5

Authors: De-Zhang Li, Xin Wang

Institutions: Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, City University of Hong Kong, City University of Hong Kong, Shenzhen Research Institute

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funders: National Natural Science Foundation of China, Shenzhen Fundamental Research Program, National Science and Technology Major Project