Current expansion and couplings for Ising lattice gauge theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918204705603584 |
|---|---|
| author | Forsström, Malin P. Viklund, Fredrik |
| author_facet | Forsström, Malin P. Viklund, Fredrik |
| contents | In this note, we discuss a random current expansion and a switching lemma for Ising lattice gauge theory at all choices of inverse temperature $β$, leading to summation over surfaces. We also describe couplings of this expansion with other representations, including the high-temperature expansion and the cluster expansion. We deduce some simple consequences, including several expressions for the Wilson loop expectation (at any $β$), a new proof of the area law estimate for sufficiently small \( β\), and a proof of exponential decay of correlations for small and large \( β. \) We also derive a few results analogous to corresponding results for the Ising model. In particular, we show that the Wilson loop expectation is non-negative at any $β$ and give an alternative short proof of Griffith's second inequality and, as a consequence, show that the Wilson loop expectations are increasing in \( β\) for all $β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Current expansion and couplings for Ising lattice gauge theory Forsström, Malin P. Viklund, Fredrik Probability In this note, we discuss a random current expansion and a switching lemma for Ising lattice gauge theory at all choices of inverse temperature $β$, leading to summation over surfaces. We also describe couplings of this expansion with other representations, including the high-temperature expansion and the cluster expansion. We deduce some simple consequences, including several expressions for the Wilson loop expectation (at any $β$), a new proof of the area law estimate for sufficiently small \( β\), and a proof of exponential decay of correlations for small and large \( β. \) We also derive a few results analogous to corresponding results for the Ising model. In particular, we show that the Wilson loop expectation is non-negative at any $β$ and give an alternative short proof of Griffith's second inequality and, as a consequence, show that the Wilson loop expectations are increasing in \( β\) for all $β$. |
| title | Current expansion and couplings for Ising lattice gauge theory |
| topic | Probability |
| url | https://arxiv.org/abs/2502.19942 |