Exact solution and high-temperature series expansion study of the one-fifth-depleted square-lattice Ising model

Simeon Hanks, Trinanjan Datta, Jaan Oitmaa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The critical behavior of the one-fifth-depleted square-lattice Ising model with nearest-neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field susceptibility. For the exact solution we employ a decoration transformation followed by a mapping to a staggered eight-vertex model. This yields a quartic equation for the critical coupling giving Kc(≡βJc)=0.695. The series expansion for the susceptibility, to O(K18), when analyzed via standard Padé approximant methods gives an estimate of Kc, consistent with the exact solution result to at least four significant figures. The series expansion is also analyzed for the leading amplitude and subdominant terms.
Original languageEnglish (US)
Article number062143
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number6
DOIs
StatePublished - Jun 28 2013

Fingerprint

High Temperature Expansion
Lattice Model
series expansion
Series Expansion
Square Lattice
Ising model
Ising Model
Exact Solution
Susceptibility
quartic equations
Most or least significant digit
magnetic permeability
Vertex Model
Critical Behavior
Quartic
Nearest Neighbor
apexes
Zero
Term
estimates

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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abstract = "The critical behavior of the one-fifth-depleted square-lattice Ising model with nearest-neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field susceptibility. For the exact solution we employ a decoration transformation followed by a mapping to a staggered eight-vertex model. This yields a quartic equation for the critical coupling giving Kc(≡βJc)=0.695. The series expansion for the susceptibility, to O(K18), when analyzed via standard Pad{\'e} approximant methods gives an estimate of Kc, consistent with the exact solution result to at least four significant figures. The series expansion is also analyzed for the leading amplitude and subdominant terms.",
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AB - The critical behavior of the one-fifth-depleted square-lattice Ising model with nearest-neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field susceptibility. For the exact solution we employ a decoration transformation followed by a mapping to a staggered eight-vertex model. This yields a quartic equation for the critical coupling giving Kc(≡βJc)=0.695. The series expansion for the susceptibility, to O(K18), when analyzed via standard Padé approximant methods gives an estimate of Kc, consistent with the exact solution result to at least four significant figures. The series expansion is also analyzed for the leading amplitude and subdominant terms.

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