Critical behaviour of random-bond Potts models: a transfer matrix study
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, 6 April 1998, Pages 701-742
Critical behaviour of random-bond Potts models: a transfer matrix study
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aUniversity of Oxford, Department of Physics - Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UKbInstitute of Physics and Astronomy, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, DenmarkcSomerville College, Oxford, UKdAll Souls College, Oxford, UK
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We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q & 4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting universality classes by combining transfer matrix data with conformal invariance. The magnetic exponent β/v varies continuously with q, assuming non-Ising values for q & 4, whereas the correlation length exponent ν is numerically consistent with unity. We present evidence for the correctness of a formerly proposed phase diagram, unifying pure, percolative and non-trivial random behaviour.
Lyapunov spectra
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, 15 April 2016, Pages 51–65
Detrital cave sediments record Late Quaternary hydrologic and climatic variability in northwestern Florida, USA, , , , , , , , a Department of Oceanography, Texas A&M University, College Station, Texas 77842, USAb Department of Marine Sciences, Texas A&M University at Galveston, Galveston, Texas 77554, USAc Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USAd Department of Chemistry, Texas A&M University, College Station, Texas 77842, USA&First stratigraphic analysis of sediments in a Floridian underwater cave.&Late Pleistocene sedimentation appears linked to lower paleo water levels.&Units of carbonate sediment with fossils likely document periods of cave expansion.&Organic-rich units likely evidence increased precipitation and riverine discharge.Detrital sediment in Florida's (USA) submerged cave systems may preserve records of regional climate and hydrologic variability. However, the basic sedimentology, mineralogy, stratigraphic variability, and emplacement history of the successions in Florida's submerged caves remains poorly understood. Here we present stratigraphic, mineralogical, and elemental data on sediment cores from two phreatic cave systems in northwestern Florida (USA), on the Dougherty Karst Plain: Hole in the Wall Cave (HITW) and Twin Cave. Water flowing through these caves is subsurface flow in the Apalachicola River drainage basin, and the caves are located just downstream from Jackson Blue (1st magnitude spring, & 2.8 m3 s& 1 discharge). Sedimentation in these caves is dominated by three primary sedimentary styles: (i) ferromanganese deposits dominate the basal recovered stratigraphy, which pass upsection into (ii) poorly sorted carbonate sediment, and finally into (iii) fine-grained organic matter (gyttja) deposits. Resolving the emplacement history of the lower stratigraphic units was hampered by a lack of suitable material for radiocarbon dating, but the upper organic-rich deposits have a punctuated depositional history beginning in the earliest Holocene. For example, gyttja primarily accumulated in HITW and Twin Caves from ~ 5500 to 3500 cal yr. BP, which coincides with regional evidence for water-table rise of the Upper Floridian Aquifer associated with relative sea-level rise in the Gulf of Mexico, and evidence for invigorated drainage through the Apalachicola River drainage basin. Gyttja sediments were also deposited in one of the caves during the B&lling/Aller&d climate oscillation. Biologically, these results indicate that some Floridian aquatic cave (stygobitic) ecosystems presently receive minimal organic matter supply in comparison to prehistoric intervals. The pre-Holocene poorly sorted carbonate sediment contains abundant invertebrate fossils, and likely documents a period of enhanced limestone dissolution and cave formation (speleogenesis) during lower paleo water levels. Further work is still required to (a) determine whether precipitation of the ferromanganese deposits is inorganically or biologically mediated, (b) temporally constrain the emplacement history of the primary sedimentary styles, and (c) determine the full geographic extent of these sedimentary signals. However, these preliminary observations suggest that sedimentation in the inland underwater caves of northwestern Florida is related to Quaternary-scale hydrographic variability in the Apalachicola River drainage basin in response to broader ocean and atmospheric forcing.KeywordsPhreatic; Karst; Florida; Apalachicola; Underwater cave
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