Jul 26 – 30, 2021
US/Eastern timezone

Clock model interpolation and symmetry breaking in O(2) models

Jul 29, 2021, 9:45 PM
Oral presentation Algorithms (including Machine Learning, Quantum Computing, Tensor Networks) Algorithms (including Machine Learning, Quantum Computing, Tensor Networks)


Leon Hostetler (Michigan State University)


The $q$-state clock model is a classical spin model that corresponds to the Ising model (when $q= 2$) and the XY model (when $q\rightarrow\infty$). The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q = 2,3,4$ and two phase transitions when $q > 4$.We define an extended-$q$ clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to non-integer $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with non-integer $q$ has a crossover and a second-order phase transition. We also define an extended-O(2) model (with a parameter $\gamma$) that reduces to the XY model when $\gamma= 0$ and to the extended-$q$ clock model when $\gamma\rightarrow\infty$, and we begin to outline the phase diagram of this model. These models with non-integer $q$ serve as a testbed to study symmetry breaking with tensor methods where experimental parameters can be tuned continuously.

Primary author

Leon Hostetler (Michigan State University)


Jin Zhang (University of Iowa) Ryo Sakai (University of Iowa) Judah Unmuth-Yockey (Fermi National Laboratory) Alexei Bazavov (Michigan State University) Yannick Meurice (University of Iowa)

Presentation materials