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Krčmár R, Šamaj L. Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal. Phys Rev E 2018; 97:012108. [PMID: 29448318 DOI: 10.1103/physreve.97.012108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Indexed: 06/08/2023]
Abstract
The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents η_{e} and δ_{e} which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.
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Affiliation(s)
- Roman Krčmár
- Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84511 Bratislava, Slovakia
| | - Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84511 Bratislava, Slovakia
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Deschner A, Sørensen ES. Valence-bond quantum Monte Carlo algorithms defined on trees. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033304. [PMID: 25314561 DOI: 10.1103/physreve.90.033304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2014] [Indexed: 06/04/2023]
Abstract
We present a class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a projective T=0 Monte Carlo method based on sampling of a set of operator strings that can be viewed as forming a treelike structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator string. In quite general terms, we derive a set of equations whose solutions correspond to a whole class of algorithms. As specific examples of this class of algorithms, we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree, and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update.
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Affiliation(s)
- Andreas Deschner
- Department of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1
| | - Erik S Sørensen
- Department of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1
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Magnetized States of Quantum Spin Chains. ACTA ACUST UNITED AC 2002. [DOI: 10.1007/3-540-45649-x_8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Barzykin V, Affleck I. Finite-size scaling for the spin-Heisenberg antiferromagnetic chain. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/32/6/001] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Eggert S. Numerical evidence for multiplicative logarithmic corrections from marginal operators. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R9612-R9615. [PMID: 9984773 DOI: 10.1103/physrevb.54.r9612] [Citation(s) in RCA: 89] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Schollwöck U, Golinelli O, Jolicœur T. S=2 antiferromagnetic quantum spin chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:4038-4051. [PMID: 9986304 DOI: 10.1103/physrevb.54.4038] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hallberg K, Wang XQ, Horsch P, Moreo A. Critical Behavior of the S=3/2 Antiferromagnetic Heisenberg Chain. PHYSICAL REVIEW LETTERS 1996; 76:4955-4958. [PMID: 10061422 DOI: 10.1103/physrevlett.76.4955] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Yamamoto S. Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:3364-3373. [PMID: 9983846 DOI: 10.1103/physrevb.53.3364] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bao SQ, Zhao H, Shen JL, Yang GZ. Thermodynamic properties of one-dimensional spin-1 antiferromagnetic Heisenberg chains: Green's-function approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:735-740. [PMID: 9983027 DOI: 10.1103/physrevb.53.735] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Wang W, Qin S, Lu ZY, Yu L, Su Z. Impurity energy level in the Haldane gap. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:40-43. [PMID: 9981936 DOI: 10.1103/physrevb.53.40] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Yamamoto S. Critical exponent eta in S=1 antiferromagnetic Heisenberg chains with alternating interaction. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:10170-10176. [PMID: 9980066 DOI: 10.1103/physrevb.52.10170] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hellberg CS, Manousakis E. Two-dimensional t-J model at low electron density. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:4639-4642. [PMID: 9981622 DOI: 10.1103/physrevb.52.4639] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hao B, Gong C. Spin correlations in low-dimensional spin-1/2 antiferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:299-304. [PMID: 9979605 DOI: 10.1103/physrevb.52.299] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Wang H, Shen J, Li K, Su Z. Low-temperature properties of a spin-1 antiferromagnetic chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:16103-16110. [PMID: 9978592 DOI: 10.1103/physrevb.51.16103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zhang WJ, Shen JL, Xu JH, Ting CS. Green's function study of one-dimensional spin-1/2 Ising-Heisenberg ferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:2950-2954. [PMID: 9979072 DOI: 10.1103/physrevb.51.2950] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Wong WH, Lo CF, Wang YL. Coupled-cluster approximation for a spin-1 Heisenberg antiferromagnet with anisotropic exchange interaction and easy-plane single-ion anisotropy. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:6126-6136. [PMID: 9976985 DOI: 10.1103/physrevb.50.6126] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Yamamoto S, Miyashita S. Anisotropy effects on the magnetic properties of an S=1 antiferromagnetic Heisenberg chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:6277-6288. [PMID: 9977004 DOI: 10.1103/physrevb.50.6277] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Golinelli O, Jolicoeur T, Lacaze R. Finite-lattice extrapolations for a Haldane-gap antiferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:3037-3044. [PMID: 9976548 DOI: 10.1103/physrevb.50.3037] [Citation(s) in RCA: 58] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Takahashi M. Excitation spectra of S=1 antiferromagnetic chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:3045-3051. [PMID: 9976549 DOI: 10.1103/physrevb.50.3045] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lopez A, Rojo AG, Fradkin E. Chern-Simons theory of the anisotropic quantum Heisenberg antiferromagnet on a square lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:15139-15158. [PMID: 10010622 DOI: 10.1103/physrevb.49.15139] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sorensen ES, Affleck I. Equal-time correlations in Haldane-gap antiferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:15771-15788. [PMID: 10010711 DOI: 10.1103/physrevb.49.15771] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sorensen ES, Affleck I. S(k) for Haldane-gap antiferromagnets: Large-scale numerical results versus field theory and experiment. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:13235-13238. [PMID: 10010248 DOI: 10.1103/physrevb.49.13235] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wang H, Shen J, Li K, Su Z. Self-consistent mean-field theory of a spin-1 antiferromagnetic chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:12805-12812. [PMID: 10010186 DOI: 10.1103/physrevb.49.12805] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chen H, Yu L, Su Z. Properties of an S=1 antiferromagnetic Heisenberg chain with single-ion anisotropy. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:12692-12697. [PMID: 10007639 DOI: 10.1103/physrevb.48.12692] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Karbach M, Mütter K, Ueberholz P, Kröger H. Approach to the spin-1/2 quantum Heisenberg model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:13666-13677. [PMID: 10007768 DOI: 10.1103/physrevb.48.13666] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Yamamoto S, Miyashita S. Thermodynamic properties of S=1 antiferromagnetic Heisenberg chains as Haldane systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:9528-9538. [PMID: 10007195 DOI: 10.1103/physrevb.48.9528] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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White SR, Huse DA. Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:3844-3852. [PMID: 10008834 DOI: 10.1103/physrevb.48.3844] [Citation(s) in RCA: 121] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sandvik AW, Scalapino DJ, Singh C. Quantum Monte Carlo study of spin correlations in the one-dimensional Hubbard model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:2112-2117. [PMID: 10008602 DOI: 10.1103/physrevb.48.2112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hellberg CS, Mele EJ. Luttinger-liquid instability in the one-dimensional t-J model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:646-649. [PMID: 10006831 DOI: 10.1103/physrevb.48.646] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Miyashita S, Yamamoto S. Effects of edges in S=1 Heisenberg antiferromagnetic chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:913-919. [PMID: 10007949 DOI: 10.1103/physrevb.48.913] [Citation(s) in RCA: 63] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Takahashi M. Elementary excitations of an anisotropic spin-1 chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:311-316. [PMID: 10006780 DOI: 10.1103/physrevb.48.311] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lu ZY, Su ZB, Yu L. Haldane energy gap of a doped linear-chain Heisenberg antiferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:12276-12279. [PMID: 10005405 DOI: 10.1103/physrevb.47.12276] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Chen YC, Lee TK. New phase in the one-dimensional t-J model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:11548-11551. [PMID: 10005307 DOI: 10.1103/physrevb.47.11548] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sandvik AW, Scalapino DJ. Correlation functions in periodic chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:12333-12336. [PMID: 10005420 DOI: 10.1103/physrevb.47.12333] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Barnes T, Dagotto E, Riera J, Swanson ES. Excitation spectrum of Heisenberg spin ladders. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:3196-3203. [PMID: 10006402 DOI: 10.1103/physrevb.47.3196] [Citation(s) in RCA: 198] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ma S, Broholm C, Reich DH, Sternlieb BJ, Erwin RW. Dominance of long-lived excitations in the antiferromagnetic spin-1 chain NENP. PHYSICAL REVIEW LETTERS 1992; 69:3571-3574. [PMID: 10046855 DOI: 10.1103/physrevlett.69.3571] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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White SR. Density matrix formulation for quantum renormalization groups. PHYSICAL REVIEW LETTERS 1992; 69:2863-2866. [PMID: 10046608 DOI: 10.1103/physrevlett.69.2863] [Citation(s) in RCA: 1484] [Impact Index Per Article: 46.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Alcaraz FC, Moreo A. Critical behavior of anisotropic spin-S Heisenberg chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:2896-2907. [PMID: 10003981 DOI: 10.1103/physrevb.46.2896] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ng TK. Schwinger-boson mean-field theory for S=1 open spin chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:8181-8184. [PMID: 10000644 DOI: 10.1103/physrevb.45.8181] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Chu D, Shen J. Self-consistent approximation for spin-1/2 quantum Heisenberg antiferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:4689-4692. [PMID: 10000134 DOI: 10.1103/physrevb.44.4689] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Mutka H, Payen C, Molinié P, Soubeyroux JL, Colombet P, Taylor AD. Dynamic structure factor. PHYSICAL REVIEW LETTERS 1991; 67:497-500. [PMID: 10044909 DOI: 10.1103/physrevlett.67.497] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Medeiros D, Cabrera GG. Numerical test of finite-size corrections for the anisotropic Heisenberg antiferromagnet chain. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:848-851. [PMID: 9999195 DOI: 10.1103/physrevb.44.848] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Sakai T, Takahashi M. S=1 antiferromagnetic Heisenberg chain in a magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:13383-13393. [PMID: 9997168 DOI: 10.1103/physrevb.43.13383] [Citation(s) in RCA: 88] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sandvik AW, Kurkijärvi J. Quantum Monte Carlo simulation method for spin systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:5950-5961. [PMID: 9997997 DOI: 10.1103/physrevb.43.5950] [Citation(s) in RCA: 200] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Medeiros D, Cabrera GG. Lanczos calculation for the s=1/2 antiferromagnetic Heisenberg chain up to N=28 spins. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:3703-3705. [PMID: 9997698 DOI: 10.1103/physrevb.43.3703] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Liang S. Existence of Néel order at T=0 in the spin-1/2 antiferromagnetic Heisenberg model on a square lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:6555-6560. [PMID: 9994742 DOI: 10.1103/physrevb.42.6555] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Deisz J, Jarrell M, Cox DL. S(q, omega ) for the S=1/2 and S=1 one-dimensional Heisenberg antiferromagnet: A quantum Monte Carlo study. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:4869-4872. [PMID: 9996043 DOI: 10.1103/physrevb.42.4869] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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