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Jorge LN, Ferreira LS, Caparica AA. Three-dimensional Baxter-Wu model. Phys Rev E 2019; 100:032141. [PMID: 31640024 DOI: 10.1103/physreve.100.032141] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2018] [Indexed: 11/07/2022]
Abstract
A classic three-dimensional spin model, based upon the Baxter-Wu scheme, is presented. It is found, by entropic sampling simulations, that the behavior of the energy and magnetization fourth-order cumulants points to a first-order phase transition. A finite-size procedure was performed, confirming that the system scales with the dimensionality d=3, yielding a high-resolution estimate of the transition temperature as T_{c}=11.377485(29).
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Affiliation(s)
- L N Jorge
- Instituto Federal do Mato Grosso, Campus Cáceres, CEP. 78200-000, Cáceres, Mato Grosso, Brazil
| | - L S Ferreira
- Instituto de Física, Universidade Federal de Goiás, Av. Esperança s/n, 74.690-900, Goiânia, GO, Brazil
| | - A A Caparica
- Instituto de Física, Universidade Federal de Goiás, Av. Esperança s/n, 74.690-900, Goiânia, GO, Brazil
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2
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Martínez-Galera AJ, Schröder UA, Huttmann F, Jolie W, Craes F, Busse C, Caciuc V, Atodiresei N, Blügel S, Michely T. Oxygen orders differently under graphene: new superstructures on Ir(111). NANOSCALE 2016; 8:1932-1943. [PMID: 26426949 DOI: 10.1039/c5nr04976h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Using scanning tunneling microscopy, the oxygen adsorbate superstructures on bare Ir(111) are identified and compared to the ones formed by intercalation in between graphene and the Ir(111) substrate. For bare Ir(111) we observe O-(2 × 2) and O-(2 × 1) structures, thereby clarifying a persistent uncertainty about the existence of these structures and the role of defects for their stability. For the case of graphene-covered Ir(111), oxygen intercalation superstructures can be imaged through the graphene monolayer by choosing proper tunneling conditions. Depending on the pressure, temperature and duration of O2 exposure as well as on the graphene morphology, O-(2 × 2), O-(√3×√3)-R30°, O-(2 × 1) and O-(2√3 × 2√3)-R30° superstructures with respect to Ir(111) are observed under the graphene cover. Two of these structures, the O-(√3 × √3)-R30° and the (2√3 × 2√3)-R30° structure are only observed when the graphene layer is on top. Phase coexistence and formation conditions of the intercalation structures between graphene and Ir(111) are analyzed. The experimental results are compared to density functional theory calculations including dispersive forces. The existence of these phases under graphene and their absence on bare Ir(111) are discussed in terms of possible changes in the adsorbate-substrate interaction due to the presence of the graphene cover.
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Affiliation(s)
| | - U A Schröder
- II. Physikalisches Institut, Universität zu Köln, Germany.
| | - F Huttmann
- II. Physikalisches Institut, Universität zu Köln, Germany.
| | - W Jolie
- II. Physikalisches Institut, Universität zu Köln, Germany.
| | - F Craes
- II. Physikalisches Institut, Universität zu Köln, Germany.
| | - C Busse
- II. Physikalisches Institut, Universität zu Köln, Germany.
| | - V Caciuc
- Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich, Germany
| | - N Atodiresei
- Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich, Germany
| | - S Blügel
- Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich, Germany
| | - T Michely
- II. Physikalisches Institut, Universität zu Köln, Germany.
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Binder K, Landau DP. Monte Carlo Calculations on Phase Transitions in Adsorbed Layers. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141250.ch3] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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Abstract
The coverage regime just beyond 0.33 ML, representative of a perfectly ordered (square root 3 x square root 3)R30 degrees-CO layer on Ru(0001), has been investigated using infrared-absorption spectroscopy. Different isotopic mixtures of CO have been employed to derive a profound understanding of structural properties of such layers. It is found that extra CO molecules incorporated into the (square root 3 x square root 3)R30 degrees-CO layer affect their nearest neighbor molecules only, and the associated density gradient extends over no more than a few angstroms. Contrary to existing belief, the model system CO on Ru(0001) does not represent a case of an unusually shallow adsorption potential corrugation. Rather, CO experiences an exceptionally strong site preference when adsorbed on Ru(0001). Annealing causes the local distortion of the overlattice to propagate laterally, most probably in a density wave-like manner. Incipient motion on the atomic scale thereby has been detected by means of isotopic labeling of inequivalent molecules within the high density areas. All major conclusions are based on observations of (isotopically labeled) minority CO species which feature negligible dynamical lateral coupling. The majority CO species, on the other hand, provide laterally averaged, unspecific information on the status of the layer.
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Affiliation(s)
- P Jakob
- Physik-Department E20, Technische Universität München, 85747 Garching, Germany.
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Alvarez J, Etgens VH, Torrelles X, Fajardo P, Ferrer S. Disordering of the low-temperature c(4 x 2) structure of Ge(001) to the (2 x 1) reconstruction: Evidence for a mean-field transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:5581-5585. [PMID: 9986521 DOI: 10.1103/physrevb.54.5581] [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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6
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Baraldi A, Dhanak VR, Comelli G, Prince KC, Rosei R. O/Rh(100) p(2 x 2)-->c(2 x 2) order-disorder phase transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:4073-4077. [PMID: 9983962 DOI: 10.1103/physrevb.53.4073] [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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Budde K, Schwenger L, Voges C, Pfnür H. Effect of oxygen impurities on the critical properties of the (2 x 2)-2H/Ni(111) order-disorder phase transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9275-9282. [PMID: 9979971 DOI: 10.1103/physrevb.52.9275] [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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Sokolowski M, Pfnür H. Phase transitions of the striped domain-wall phases of S on Ru(0001). PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:15742-15751. [PMID: 9978551 DOI: 10.1103/physrevb.51.15742] [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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9
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Chapter III Phase transitions at surfaces. ACTA ACUST UNITED AC 1995. [DOI: 10.1016/s0922-7725(06)80004-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Schwenger L, Budde K, Voges C, Pfnür H. Effect of random quenched impurities on the critical behavior of a four-state Potts system in two dimensions: An experimental study. PHYSICAL REVIEW LETTERS 1994; 73:296-299. [PMID: 10057134 DOI: 10.1103/physrevlett.73.296] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Sokolowski M, Pfnür H. Continuous order-disorder phase transitions of the p(2 x 2) and ( sqrt 3 x sqrt 3 )R30( degrees) superstructures of sulfur on Ru(001): Effective critical exponents and finite-size effects. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:7716-7728. [PMID: 10009518 DOI: 10.1103/physrevb.49.7716] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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12
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Feng YP, Chan MH. Continuous orientational ordering transition of carbon monoxide on graphite. PHYSICAL REVIEW LETTERS 1993; 71:3822-3825. [PMID: 10055082 DOI: 10.1103/physrevlett.71.3822] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Baek DH, Chung JW, Han WK. Critical behavior of the p(2 x 1)-O/W(110) system. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:8461-8464. [PMID: 10004881 DOI: 10.1103/physrevb.47.8461] [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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14
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Zuo J, Zehner DM. Terrace-width and step-height enlargement: Reconstruction of the TaC(310) surface. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:16122-16127. [PMID: 10003750 DOI: 10.1103/physrevb.46.16122] [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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Pfnür H, Piercy P. Oxygen on Ru(001): Critical behavior of a p(2 x 1) order-disorder transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:582-589. [PMID: 9992797 DOI: 10.1103/physrevb.41.582] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Grzelakowski K, Lyuksyutov I, Bauer E. Direct observation of scaling by high-resolution low-energy electron diffraction: O on Mo(110). PHYSICAL REVIEW LETTERS 1990; 64:32-35. [PMID: 10041266 DOI: 10.1103/physrevlett.64.32] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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17
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The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers. ACTA ACUST UNITED AC 1989. [DOI: 10.1007/bf01453796] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Pfnür H, Piercy P. Critical behavior of p(2 x 2) oxygen on Ru(001): An example of four-state Potts critical exponents. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:2515-2522. [PMID: 9992139 DOI: 10.1103/physrevb.40.2515] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sokolowski M, Pfnür H. Influence of steps on the critical behavior of a two-dimensional system: p(2 x 2) oxygen on a stepped Ru(0001) surface. PHYSICAL REVIEW LETTERS 1989; 63:183-186. [PMID: 10040801 DOI: 10.1103/physrevlett.63.183] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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20
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Fan WC, Ignatiev A, Hu B. Order-disorder critical behavior of orientationally ordered incommensurate overlayers of cesium and potassium on the Cu(111) surface. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:6816-6818. [PMID: 9947327 DOI: 10.1103/physrevb.39.6816] [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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