TY - JOUR

T1 - Lattice Gauge Theory and a Random-Medium Ising Model

AU - Skopenkov, Mikhail

N1 - KAUST Repository Item: Exported on 2022-09-14
Acknowledgements: The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement N075-15-2019-1619.
For the latter conjecture, there have been suggested a proof by K. Izyurov and A. Magazinov, as well as interesting generalizations by M. Fedorov and I. Novikov (private communication) [16 , 17]. The author is grateful to D. Chelkak, H. Duminil-Copin, M. Khristoforov, S. Melikhov, S. Smirnov for useful discussions.

PY - 2022/7/6

Y1 - 2022/7/6

N2 - We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

AB - We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

UR - http://hdl.handle.net/10754/679668

UR - https://link.springer.com/10.1007/s11040-022-09430-9

UR - http://www.scopus.com/inward/record.url?scp=85133553929&partnerID=8YFLogxK

U2 - 10.1007/s11040-022-09430-9

DO - 10.1007/s11040-022-09430-9

M3 - Article

SN - 1572-9656

VL - 25

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

IS - 3

ER -