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Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

Publication ,  Journal Article
Hu, Y; Charbonneau, P
Published in: Physical Review B
October 1, 2021

Ising models with frustrated next-nearest-neighbor interactions present a rich array of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational study. In two dimensions, strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method, which bypasses both difficulties, can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau, Phys. Rev. B 103, 094441 (2021)2469-995010.1103/PhysRevB.103.094441], in which we evaluated the two-dimensional axial next-nearest-neighbor Ising model with transfer matrices, we here extend the effective usage of the TM method to Ising models with biaxial, diagonal, and third-nearest-neighbor frustration models. The high-accuracy TM numerics help resolve various physical ambiguities about these reference models, thus providing a clearer overview of modulated phase formation in two dimensions.

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Published In

Physical Review B

DOI

EISSN

2469-9969

ISSN

2469-9950

Publication Date

October 1, 2021

Volume

104

Issue

14

Related Subject Headings

  • 51 Physical sciences
  • 40 Engineering
  • 34 Chemical sciences
 

Citation

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Hu, Y., & Charbonneau, P. (2021). Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices. Physical Review B, 104(14). https://doi.org/10.1103/PhysRevB.104.144429
Hu, Y., and P. Charbonneau. “Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices.” Physical Review B 104, no. 14 (October 1, 2021). https://doi.org/10.1103/PhysRevB.104.144429.
Hu, Y., and P. Charbonneau. “Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices.” Physical Review B, vol. 104, no. 14, Oct. 2021. Scopus, doi:10.1103/PhysRevB.104.144429.

Published In

Physical Review B

DOI

EISSN

2469-9969

ISSN

2469-9950

Publication Date

October 1, 2021

Volume

104

Issue

14

Related Subject Headings

  • 51 Physical sciences
  • 40 Engineering
  • 34 Chemical sciences