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Dual Z_2 Lattice Gauge Theory of the 3D Ising Model with both Nearest- and Next-Nearest-Neighbor Couplings

Peng, Changnan (2018) Dual Z_2 Lattice Gauge Theory of the 3D Ising Model with both Nearest- and Next-Nearest-Neighbor Couplings. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190130-121849382

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Abstract

It is known that the normal three-dimensional (3D) Ising model on a cubic lattice is dual to the Wegner's 3D Z_2 lattice gauge theory. Here we find an unusual Z_2 lattice gauge theory which is dual to the 3D Ising model with not only nearest-neighbor (nn) coupling, but also next-nearest-neighbor (nnn) coupling. Our gauge theory has on each edge four Z_2 variables that have product +1, each located on a vector perpendicular to the edge. The nn coupling in the Ising model maps to the plaquette term in the gauge theory where the four variables multiplied have their vectors pointing inward, while the nnn coupling maps to the coupling between the Z_2 variables on nearby vectors on each edge in the gauge theory. A Wilson loop observable in the gauge theory depends on a framing of a loop, and maps to a surface of flipped-sign nn and nnn couplings in the Ising model. Further numerical simulations could be made to explore the universality at the phase transition.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1812.02938arXivDiscussion Paper
Alternate Title:Dual Z2 Lattice Gauge Theory of the 3D Ising Model with both Nearest- and Next-Nearest-Neighbor Couplings
Additional Information:The author would like to express sincere gratitude to the mentor Prof. Anton Kapustin for the guidance. This work was supported by the Caltech SURF program. The author acknowledges the generous support of Dr. Neher and his family. Thanks to Yu-An Chen for many fruitful discussion. Some computations in this project were conducted on the Caltech High Performance Computing Cluster.
Funders:
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Record Number:CaltechAUTHORS:20190130-121849382
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190130-121849382
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92520
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:31 Jan 2019 01:00
Last Modified:31 Jan 2019 01:00

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