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Relationship among Exactly Soluble Models of Critical Phenomena. I: 2D Ising Model, Dimer Problem and the Generalized XY-Model
Abstract
By relating a transfer matrix associated with a classical system to the Hamiltonian of its corresponding quantum mechanical system, it is proved that the two-dimensional Ising model in the absence of a magnetic field is equivalent to the ground state of the linear XY-model in the presence of a magnetic field, under appropriate relations among coupling parameters appearing in the two Hamiltonians. Simple relations are established for spin correlations in both systems. Consequently, the Ising system and the ground state of the XY-model are shown to exhibit similar singularities with respect to temperature and a magnetic field, respectively. It is also proved that the two-dimensional dimer problem is equivalent to the ground state of a generalized XY-model, which is solved exactly in general.
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Citations
Cited by
Suzuki, M. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01609348 · Cited by 895
Self-citationUniversality classes in nonequilibrium lattice systems
Ódor, G. (2004) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.663 · Cited by 835
Mathematical foundation of quantum annealing
Morita, S., & Nishimori, H. (2008) · Journal of Mathematical Physics · doi:10.1063/1.2995837 · Cited by 381
Cluster Monte Carlo simulation of the transverse Ising model
Blöte, H. W. J., & Deng, Y. (2002) · Physical Review E · doi:10.1103/physreve.66.066110 · Cited by 284
Rams, M. M., Czarnik, P., & Cincio, L. (2018) · Physical Review X · doi:10.1103/physrevx.8.041033 · Cited by 81
Metadata
- Authors
- Suzuki, M.
- Venue
- Progress of Theoretical Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 1971-11
- Volume
- 46
- Issue
- 5
- Pages
- 1337-1359
- ISSN
- 0033-068X (ISSN-L)
- OpenAlex
- W2045966288
- Cited by
- 277
- References
- 0
- FWCI
- 2.26
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Relationship among Exactly Soluble Models of Critical Phenomena. I: 2D Ising Model, Dimer Problem and the Generalized XY-Model. https://app.cochat.ai/papers/10.1143/ptp.46.1337
- The paper
- Suzuki, M. (1971). Relationship among Exactly Soluble Models of Critical Phenomena. I: 2D Ising Model, Dimer Problem and the Generalized XY-Model. Progress of Theoretical Physics. https://doi.org/10.1143/ptp.46.1337
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