51
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Vannimenus J, Maillard JM, Seze LD. Ground-state correlations in the two-dimensional Ising frustration model. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/12/21/019] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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52
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Hartmann AK. Ground-state clusters of two-, three-, and four-dimensional +/-J Ising spin glasses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:016106. [PMID: 11304313 DOI: 10.1103/physreve.63.016106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2000] [Indexed: 05/23/2023]
Abstract
A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +/-J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20(2),8(3),6(4) spins are treated. A "ballistic-search" algorithm is applied, which allows even for large system sizes to identify clusters of ground states that are connected by chains of zero-energy flips of spins. The number of clusters n(C) diverges with N going to infinity. For all dimensions considered here, an exponential increase of n(C) appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s(0)=0.078(5)k(B) (2D), s(0)=0.051(3)k(B) (3D), respectively, s(0)=0.027(5)k(B) (4D) is obtained.
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Affiliation(s)
- A K Hartmann
- Institut für Theoretische Physik, Bunsenstrasse 9, 37073 Göttingen, Germany.
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53
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Tanaka F, Edwards SF. Analytic theory of the ground state properties of a spin glass. I. Ising spin glass. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0305-4608/10/12/017] [Citation(s) in RCA: 103] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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54
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Blackman JA, Kemeny G, Straley JP. Absence of spin glass order in the 2D site-diluted triangular antiferromagnet. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/14/4/014] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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55
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Almeida JRLD, Fittipaldi IP, Barreto FCS. On the ferromagnetic phase breakdown of a two-dimensional Ising model with competing interactions. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/14/13/004] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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57
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Kolan AJ, Palmer RG. Distribution of frustrated plaquettes in the random bond square lattice. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/13/23/002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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58
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Guilmin P, Turban L. Cluster extension of the effective-interaction approximation. I. Quenched-bond disorder in the Ising model. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/13/21/013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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59
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Southern BW, Chui ST, Forgacs G. Non-universality for two-dimensional frustrated lattices? ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/13/30/001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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60
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Cheung HF, McMillan WL. Equilibrium properties of the two-dimensional random (+or-J) Ising model. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/16/36/017] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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61
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Diep HT, Lallemand P, Nagai O. Critical properties of a simple cubic fully frustrated Ising lattice by Monte Carlo method. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/18/5/013] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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62
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Curado EM, Nobre FD, Coutinho S. Ground-state degeneracies of Ising spin glasses on diamond hierarchical lattices. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3761-70. [PMID: 11970209 DOI: 10.1103/physreve.60.3761] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/1998] [Revised: 05/10/1999] [Indexed: 11/07/2022]
Abstract
The total number of ground states for short-range Ising spin glasses, defined on diamond hierarchical lattices of fractal dimensions d=2, 3, 4, 5, and 2.58, is estimated by means of analytic calculations (three last hierarchy levels of the d=2 lattice) and numerical simulations (lower hierarchies for d=2 and all remaining cases). It is shown that in the case of continuous probability distributions for the couplings, the number of ground states is finite in the thermodynamic limit. However, for a bimodal probability distribution (+/-J with probabilities p and 1-p, respectively), the average number of ground states is maximum for a wide range of values of p around p=1 / 2 and depends on the total number of sites at hierarchy level n, Nn. In this case, for all lattices investigated, it is shown that the ground-state degeneracy behaves like exp[h(d)Nn], in the limit Nn large, where h(d) is a positive number which depends on the lattice fractal dimension. The probability of finding frustrated cells at a given hierarchy level n, Fn(p), is calculated analytically (three last hierarchy levels for d=2 and the last hierarchy of the d=3 lattice, with 0<or=p<or=1), as well as numerically (all other cases, with p=1 / 2). Except for d=2, in which case Fn(1 / 2) increases by decreasing the hierarchy level, all other dimensions investigated present an exponential decrease in Fn(1 / 2) for decreasing values of n. For d=2 our results refer to the paramagnetic phase, whereas for all other dimensions considered [which are greater than the lower critical dimension dl (dl approximately 2.5)], our results refer to the spin-glass phase at zero temperature; in the latter cases h(d) increases with the fractal dimension. For n>>1, only the last hierarchies contribute significantly to the ground-state degeneracy; such a dominant behavior becomes stronger for high fractal dimensions. The exponential increase of the number of ground states with the total number of sites is in agreement with the mean-field picture of spin glasses.
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Affiliation(s)
- E M Curado
- Centro Brasiliro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
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64
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Longa L, Oles AM. Rigorous properties of the two-dimensional Ising model with periodically distributed frustration. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/13/3/036] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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65
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Barahona F, Maynard R, Rammal R, Uhry JP. Morphology of ground states of two-dimensional frustration model. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/15/2/033] [Citation(s) in RCA: 132] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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66
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Bieche L, Uhry JP, Maynard R, Rammal R. On the ground states of the frustration model of a spin glass by a matching method of graph theory. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/13/8/005] [Citation(s) in RCA: 126] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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67
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Freund H, Grassberger P. The ground state of the +or-J spin glass from a heuristic matching algorithm. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/22/18/036] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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69
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Müller A, Peters F, Pope MT, Gatteschi D. Polyoxometalates: Very Large Clusters-Nanoscale Magnets. Chem Rev 1998; 98:239-272. [PMID: 11851505 DOI: 10.1021/cr9603946] [Citation(s) in RCA: 1165] [Impact Index Per Article: 44.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Achim Müller
- Dipartimento di Chimica, Universitá di Firenze, Via G. Capponi 9, 50121 Firenze, Italy
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70
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Gatteschi D, Sessoli R, Plass W, Müller A, Krickemeyer E, Meyer J, Sölter D, Adler P. Giant Clusters with Unusual Electronic and Magnetic Structures Due to Open Shell Metal Centers Embedded Far Apart from Each Other: Spin Frustration and Antisymmetric Exchange. Inorg Chem 1996. [DOI: 10.1021/ic951085l] [Citation(s) in RCA: 72] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Dante Gatteschi
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Roberta Sessoli
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Winfried Plass
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Achim Müller
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Erich Krickemeyer
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Jochen Meyer
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Dirk Sölter
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
| | - Peter Adler
- Dipartimento di Chimica, Università di Firenze, I-50144 Firenze, Italy, Fakultät für Chemie, Lehrstuhl für Anorganische Chemie I, Universität Bielefeld, D-33501 Bielefeld, Germany, and Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
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71
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Gatteschi D, Tsukerblat BS. Symmetry breaking and effective motional averaging in double triangular clusters with exchange and electron transfer effects. Chem Phys 1996. [DOI: 10.1016/0301-0104(95)00239-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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72
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Kobe S, Klotz T. Frustration: How it can be measured. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:5660-5663. [PMID: 9964065 DOI: 10.1103/physreve.52.5660] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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73
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Gatteschi D, Caneschi A, Pardi L, Sessoli R. Large Clusters of Metal Ions: The Transition from Molecular to Bulk Magnets. Science 1994; 265:1054-8. [PMID: 17832894 DOI: 10.1126/science.265.5175.1054] [Citation(s) in RCA: 747] [Impact Index Per Article: 24.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Clusters of metal ions are a class of compounds actively investigated for their magnetic properties, which should gradually change from those of simple paramagnets to those of bulk magnets. However, their interest lies in a number of different disciplines: chemistry, which seeks new synthetic strategies to make larger and larger clusters in a controlled manner; physics, which can test the validity of quantum mechanical approaches at the nanometer scale; and biology, which can use them as models of biomineralization of magnetic particles.
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Péntek Á, Toroczkai Z, Mayer DH, Tél T. Kac model from a dynamical system's point of view. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:2026-2040. [PMID: 9961443 DOI: 10.1103/physreve.49.2026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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75
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Vogel EE, Cartes J, Contreras S, Lebrecht W, Villegas J. Ground-state properties of finite square and triangular Ising lattices with mixed exchange interactions. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:6018-6027. [PMID: 10011581 DOI: 10.1103/physrevb.49.6018] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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76
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Lacorre P, Pannetier J, Pebler J, Nagel S, Babel D, de Kozak A, Samouël M, Férey G. Ordered magnetic frustration: XVII. Is BaMnFeF7 frustrated? Mössbauer spectroscopy, magnetic susceptibility, and magnetic structure at 2 K. J SOLID STATE CHEM 1992. [DOI: 10.1016/0022-4596(92)90185-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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77
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Blackman JA, Poulter J. Gauge-invariant method for the +/-J spin-glass model. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:4374-4386. [PMID: 10000087 DOI: 10.1103/physrevb.44.4374] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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78
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Lin JC. Dynamic mean-field approximation for the random-bond Ising-spin model. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:13638-13640. [PMID: 9997205 DOI: 10.1103/physrevb.43.13638] [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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79
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Wang JS, Swendsen RH. Low-temperature properties of the. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:4840-4844. [PMID: 9946877 DOI: 10.1103/physrevb.38.4840] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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80
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Aharony A, Birgeneau RJ, Coniglio A, Kastner MA, Stanley HE. Magnetic phase diagram and magnetic pairing in doped La2CuO. PHYSICAL REVIEW LETTERS 1988; 60:1330-1333. [PMID: 10038007 DOI: 10.1103/physrevlett.60.1330] [Citation(s) in RCA: 193] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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81
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Sarmento EF, Muniz RB, Cavalcanti SB. Magnetization in a quenched random-bond transverse Ising model with competing interactions. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:529-535. [PMID: 9942070 DOI: 10.1103/physrevb.36.529] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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82
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Georges A, Hansel D, Le Doussal P, Maillard J, Bouchaud J. Rigorous bounds for 2D disordered ising models. ACTA ACUST UNITED AC 1986. [DOI: 10.1051/jphys:01986004706094700] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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83
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Chapter 52 Amorphous alloys. ACTA ACUST UNITED AC 1984. [DOI: 10.1016/s0168-1273(84)07005-7] [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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Wolff WF, Zittartz J. Inhomogeneous Ising models with diagonal structure on a square lattice. ACTA ACUST UNITED AC 1981. [DOI: 10.1007/bf01292658] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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90
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91
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92
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93
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Derrida B, Maillard J, Vannimenus J, Kirkpatrick S. Interface entropy and phase transitions in frustrated ising systems. ACTA ACUST UNITED AC 1978. [DOI: 10.1051/jphyslet:019780039023046500] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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