Ising ferromagnets and antiferromagnets in an imaginary magnetic field.

Title: Ising ferromagnets and antiferromagnets in an imaginary magnetic field.
Speaker: Dr. Roman Krčmár (Institute of Physics, SAV)
Start Date/Time: 2022-11-02 / 10:30 (Taipei time)
End Date/Time: 2022-11-02 / 11:30
Host : Prof. Ying-Jer Kao (Department of Physics, NTU)

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We will present results of our study of classical Ising spin-1/2 models on the 2D square lattice with ferromagnetic or antiferro- magnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The transformations of the complex Boltzmann weights of spin configurations onto symmetric vertex models which leads to real (positive or negative) Boltzmann weights will be presented. This enables us to apply accurate numerical methods based on the real space renormalization, namely the corner transfer matrix renormalization group (CTMRG) and the higher-order tensor renormalization group (HOTRG). For the 2D antiferromagnet, the curve of critical points related to the symmetry breaking of magnetizations was calculated. The critical exponent β and the central charge c are shown to be constant along the critical line, equal to their values β = 1/8 and c = 1/2 for the 2D Ising in a zero magnetic field. The 2D ferromagnets behave in analogy with their 1D counterparts defined on a chain of sites, namely there exists a transient temperature which splits the temperature range into its high-temperature and low-temperature parts. The free energy and the magnetization are well defined in the high-temperature region. In the low-temperature region, the free energy exhibits singularities at the Yang-Lee zeros of the partition function and the magnetization is also ill-defined: it varies chaotically with the size of the system. The transient temperature is determined as a function of the imaginary magnetic field by using the fact that from the high- temperature side both the first derivative of the free energy with respect to the temperature and the magnetization diverge at this temperature. 

Work was published in Physical Review E 105 054112 (2022).