Scaling Structures of Free-Energy Fluctuations in a One-Dimensional Dilute Ising Model

Abstract A linear chain of T-e molecules exhibiting the cooperative Jahn-Teller effect is considered. Following Nauenberg's1 treatment of the one-dimensional Ising model a renormalization group approach is used. The series-expansion of the free energy is put into a closed form.

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Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy

10.21468/scipostphys.5.6.059 ◽

2018 ◽

Vol 5 (6) ◽

Cited By ~ 4

Author(s):

Satoshi Ejima ◽

Tomoki Yamaguchi ◽

Fabian Essler ◽

Florian Lange ◽

Yukinori Ohta ◽

...

Keyword(s):

Phase Transitions ◽

Ising Model ◽

Critical Point ◽

Phase Structure ◽

Quantum Phase Transitions ◽

Universality Class ◽

Quantum Magnets ◽

One Dimensional ◽

Xxz Chain ◽

Dilute Ising Model

We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.

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Free-energy fluctuations in a one-dimensional random Ising model

Physical Review A ◽

10.1103/physreva.39.3170 ◽

1989 ◽

Vol 39 (6) ◽

pp. 3170-3172 ◽

Cited By ~ 15

Author(s):

Toshijiro Tanaka ◽

Hirokazu Fujisaka ◽

Masayoshi Inoue

Keyword(s):

Free Energy ◽

Ising Model ◽

One Dimensional ◽

Random Ising Model

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Investigation of magnetic field effect on surface and finite-site free energy in one-dimensional Ising model of nanosystems

Phase Transitions ◽

10.1080/01411594.2010.548755 ◽

2011 ◽

Vol 84 (7) ◽

pp. 613-623 ◽

Cited By ~ 1

Author(s):

Farid Taherkhani ◽

Hadi Abroshan ◽

Hamed Akbarzadeh ◽

Gholamabbas Parsafar ◽

Alessandro Fortunelli

Keyword(s):

Magnetic Field ◽

Free Energy ◽

Ising Model ◽

Field Effect ◽

Magnetic Field Effect ◽

One Dimensional

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Correlation functions of the one-dimensional random-field Ising model at zero temperature

Physical Review B ◽

10.1103/physrevb.48.9508 ◽

1993 ◽

Vol 48 (13) ◽

pp. 9508-9514 ◽

Cited By ~ 7

Author(s):

Edward Farhi ◽

Sam Gutmann

Keyword(s):

Ising Model ◽

Random Field ◽

Correlation Functions ◽

Zero Temperature ◽

Random Field Ising Model ◽

One Dimensional ◽

The One

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The bulk, surface and corner free energies of the anisotropic triangular Ising model

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0713 ◽

2020 ◽

Vol 476 (2234) ◽

pp. 20190713

Author(s):

Rodney J. Baxter

Keyword(s):

Free Energy ◽

Ising Model ◽

Partition Function ◽

Temperature Series ◽

Isotropic Case ◽

Series Expansions ◽

Exact Results ◽

Free Energies ◽

Bulk Surface ◽

Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

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