The critical behaviour of two-dimensional self-avoiding random walks View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1982-09

AUTHORS

P. Grassberger

ABSTRACT

We present exact results for the mean end-to-end distance of self-avoiding random walks on several planar lattices. For the square lattice, we extend the known results from walks with ≦20 steps to walks with ≦22 steps, and for the triagular lattice from 14 to 16 steps. For the honeycomb lattice we went up to 34 steps, for the two-choice square lattice up to 44 steps, and for the 4-choice triagular lattice up to 19 steps. The extrapolated valuev=0.747±0.001 (provided the correction-to-scalng exponent is not appreaciably smaller than unity) is in disagreement with both Flory's value and the recent estimate of Derrida. We claim that a different analysis of Derrida's data supports this value. More... »

PAGES

255-260

References to SciGraph publications

  • 1981-12. Monte Carlo renormalization of hard sphere polymer chains in two to five dimensions in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01420588

    DOI

    http://dx.doi.org/10.1007/bf01420588

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1047895915


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1402", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Applied Economics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/14", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Economics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Wuppertal", 
              "id": "https://www.grid.ac/institutes/grid.7787.f", 
              "name": [
                "Fachbereich 8-Physik, Universit\u00e4t Wuppertal, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Grassberger", 
            "givenName": "P.", 
            "id": "sg:person.0704113004.84", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0704113004.84"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01292850", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041787225", 
              "https://doi.org/10.1007/bf01292850"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01292850", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041787225", 
              "https://doi.org/10.1007/bf01292850"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-1573(76)90028-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052856063"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-1573(76)90028-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052856063"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1730021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057796441"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/14/1/002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059065430"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/4/4/007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059080081"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/6/3/009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059080457"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/7/4/012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059080804"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.16.1253", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060522731"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.16.1253", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060522731"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.21.3976", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060527268"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.21.3976", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060527268"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1982-09", 
        "datePublishedReg": "1982-09-01", 
        "description": "We present exact results for the mean end-to-end distance of self-avoiding random walks on several planar lattices. For the square lattice, we extend the known results from walks with \u226620 steps to walks with \u226622 steps, and for the triagular lattice from 14 to 16 steps. For the honeycomb lattice we went up to 34 steps, for the two-choice square lattice up to 44 steps, and for the 4-choice triagular lattice up to 19 steps. The extrapolated valuev=0.747\u00b10.001 (provided the correction-to-scalng exponent is not appreaciably smaller than unity) is in disagreement with both Flory's value and the recent estimate of Derrida. We claim that a different analysis of Derrida's data supports this value.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf01420588", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1285002", 
            "issn": [
              "0722-3277", 
              "1431-584X"
            ], 
            "name": "Zeitschrift f\u00fcr Physik B Condensed Matter", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "48"
          }
        ], 
        "name": "The critical behaviour of two-dimensional self-avoiding random walks", 
        "pagination": "255-260", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "e429fa9f9f9727819ab0e270ba3ecee89a1b0b2edca4da9cba32a62bd9099f23"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf01420588"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1047895915"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf01420588", 
          "https://app.dimensions.ai/details/publication/pub.1047895915"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T13:31", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000370_0000000370/records_46757_00000002.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/BF01420588"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf01420588'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf01420588'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01420588'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01420588'


     

    This table displays all metadata directly associated to this object as RDF triples.

    89 TRIPLES      21 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf01420588 schema:about anzsrc-for:14
    2 anzsrc-for:1402
    3 schema:author N45cd5d8701a24d42ab4babad701b54fc
    4 schema:citation sg:pub.10.1007/bf01292850
    5 https://doi.org/10.1016/0370-1573(76)90028-4
    6 https://doi.org/10.1063/1.1730021
    7 https://doi.org/10.1088/0305-4470/14/1/002
    8 https://doi.org/10.1088/0305-4470/4/4/007
    9 https://doi.org/10.1088/0305-4470/6/3/009
    10 https://doi.org/10.1088/0305-4470/7/4/012
    11 https://doi.org/10.1103/physrevb.16.1253
    12 https://doi.org/10.1103/physrevb.21.3976
    13 schema:datePublished 1982-09
    14 schema:datePublishedReg 1982-09-01
    15 schema:description We present exact results for the mean end-to-end distance of self-avoiding random walks on several planar lattices. For the square lattice, we extend the known results from walks with ≦20 steps to walks with ≦22 steps, and for the triagular lattice from 14 to 16 steps. For the honeycomb lattice we went up to 34 steps, for the two-choice square lattice up to 44 steps, and for the 4-choice triagular lattice up to 19 steps. The extrapolated valuev=0.747±0.001 (provided the correction-to-scalng exponent is not appreaciably smaller than unity) is in disagreement with both Flory's value and the recent estimate of Derrida. We claim that a different analysis of Derrida's data supports this value.
    16 schema:genre research_article
    17 schema:inLanguage en
    18 schema:isAccessibleForFree false
    19 schema:isPartOf N69bf07c06270477491ab63d011608cde
    20 Nb9a63b81f4454aeb80a98be32ba48dcd
    21 sg:journal.1285002
    22 schema:name The critical behaviour of two-dimensional self-avoiding random walks
    23 schema:pagination 255-260
    24 schema:productId N2bb461960fb346219ea38f99002ab3ff
    25 N39b968ad5011498f9666e142d703de29
    26 Ne412a4abeeed4625a022e46cbbceae2b
    27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047895915
    28 https://doi.org/10.1007/bf01420588
    29 schema:sdDatePublished 2019-04-11T13:31
    30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    31 schema:sdPublisher N9c192c1d5b5547f587dd1e9c049d507a
    32 schema:url http://link.springer.com/10.1007/BF01420588
    33 sgo:license sg:explorer/license/
    34 sgo:sdDataset articles
    35 rdf:type schema:ScholarlyArticle
    36 N2bb461960fb346219ea38f99002ab3ff schema:name dimensions_id
    37 schema:value pub.1047895915
    38 rdf:type schema:PropertyValue
    39 N39b968ad5011498f9666e142d703de29 schema:name readcube_id
    40 schema:value e429fa9f9f9727819ab0e270ba3ecee89a1b0b2edca4da9cba32a62bd9099f23
    41 rdf:type schema:PropertyValue
    42 N45cd5d8701a24d42ab4babad701b54fc rdf:first sg:person.0704113004.84
    43 rdf:rest rdf:nil
    44 N69bf07c06270477491ab63d011608cde schema:volumeNumber 48
    45 rdf:type schema:PublicationVolume
    46 N9c192c1d5b5547f587dd1e9c049d507a schema:name Springer Nature - SN SciGraph project
    47 rdf:type schema:Organization
    48 Nb9a63b81f4454aeb80a98be32ba48dcd schema:issueNumber 3
    49 rdf:type schema:PublicationIssue
    50 Ne412a4abeeed4625a022e46cbbceae2b schema:name doi
    51 schema:value 10.1007/bf01420588
    52 rdf:type schema:PropertyValue
    53 anzsrc-for:14 schema:inDefinedTermSet anzsrc-for:
    54 schema:name Economics
    55 rdf:type schema:DefinedTerm
    56 anzsrc-for:1402 schema:inDefinedTermSet anzsrc-for:
    57 schema:name Applied Economics
    58 rdf:type schema:DefinedTerm
    59 sg:journal.1285002 schema:issn 0722-3277
    60 1431-584X
    61 schema:name Zeitschrift für Physik B Condensed Matter
    62 rdf:type schema:Periodical
    63 sg:person.0704113004.84 schema:affiliation https://www.grid.ac/institutes/grid.7787.f
    64 schema:familyName Grassberger
    65 schema:givenName P.
    66 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0704113004.84
    67 rdf:type schema:Person
    68 sg:pub.10.1007/bf01292850 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041787225
    69 https://doi.org/10.1007/bf01292850
    70 rdf:type schema:CreativeWork
    71 https://doi.org/10.1016/0370-1573(76)90028-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052856063
    72 rdf:type schema:CreativeWork
    73 https://doi.org/10.1063/1.1730021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057796441
    74 rdf:type schema:CreativeWork
    75 https://doi.org/10.1088/0305-4470/14/1/002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059065430
    76 rdf:type schema:CreativeWork
    77 https://doi.org/10.1088/0305-4470/4/4/007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059080081
    78 rdf:type schema:CreativeWork
    79 https://doi.org/10.1088/0305-4470/6/3/009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059080457
    80 rdf:type schema:CreativeWork
    81 https://doi.org/10.1088/0305-4470/7/4/012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059080804
    82 rdf:type schema:CreativeWork
    83 https://doi.org/10.1103/physrevb.16.1253 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060522731
    84 rdf:type schema:CreativeWork
    85 https://doi.org/10.1103/physrevb.21.3976 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060527268
    86 rdf:type schema:CreativeWork
    87 https://www.grid.ac/institutes/grid.7787.f schema:alternateName University of Wuppertal
    88 schema:name Fachbereich 8-Physik, Universität Wuppertal, Germany
    89 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...