# The 38th International Symposium on Lattice Field Theory

Jul 26 – 30, 2021
US/Eastern timezone

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

Jul 29, 2021, 9:45 PM
15m
Oral presentation Algorithms (including Machine Learning, Quantum Computing, Tensor Networks)

### Speaker

Leon Hostetler (Michigan State University)

### Description

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)

### Co-authors

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

 296_R4Al_Leon_Hostetler hostetler.pdf