Transition point of the random Ising model with bond dilution

Hidetoshi Nishimori

doi:10.1088/0022-3719/12/17/001

Transition point of the random Ising model with bond dilution

Hidetoshi Nishimori

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

The transition point of the random Ising model on the square lattice is exactly calculated under the assumption of quenched randomness of bond defects. The author makes use of a duality transformation and the replica method. The transition point thus obtained is given by exp(-2K_c)=exp((1-1/2p)ln2) -1 which satisfies the boundary conditions: T_c to 0 as p to p _c=¹/₂; and K_c to ¹/ ₂ln( square root 2+1) as p to 1.

Original language	English
Article number	001
Pages (from-to)	L641-L644
Journal	Journal of Physics C: Solid State Physics
Volume	12
Issue number	17
DOIs	https://doi.org/10.1088/0022-3719/12/17/001
Publication status	Published - 1979 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Condensed Matter Physics
Engineering(all)
Physics and Astronomy(all)

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10.1088/0022-3719/12/17/001

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AB - The transition point of the random Ising model on the square lattice is exactly calculated under the assumption of quenched randomness of bond defects. The author makes use of a duality transformation and the replica method. The transition point thus obtained is given by exp(-2Kc)=exp((1-1/2p)ln2) -1 which satisfies the boundary conditions: Tc to 0 as p to p c=1/2; and Kc to 1/ 2ln( square root 2+1) as p to 1.

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Transition point of the random Ising model with bond dilution

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