Possible failure of asymptotic freedom in two-dimensional RP2 and RP3 σ-models

Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We have simulated the two-dimensional RP2 and RP3 σ-models, at correlation lengths up to about 220 (resp. 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the conventional asymptotic scaling scenario at all correlation lengths less than about 109 (resp. 105). Moreover, they are consistent with a critical point at β ≈ 5.70 (resp. 6.96), only 2% (resp. 5%) beyond the largest β at which we ran. Preliminary studies of a mixed SN-1 RPN-1 model (i.e. isovector + isotensor action) show a similar freedom behavior when βT → ∞ with βV fixed {less-than or approximate} 0.6, while they are consistent with conventional asymptotic freedom along the lines βT βV fixed {less-than or approximate} 2. Taken as a whole, the data cast doubt on (though they do not completely exclude) the idea that RPN-1 and SN-1 σ-models lie in the same universality class.

    Original languageEnglish (US)
    Pages (from-to)815-818
    Number of pages4
    JournalNuclear Physics B - Proceedings Supplements
    Volume30
    Issue numberC
    DOIs
    StatePublished - 1993

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    scaling
    embedding
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    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

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    Possible failure of asymptotic freedom in two-dimensional RP2 and RP3 σ-models. / Caracciolo, Sergio; Edwards, Robert G.; Pelissetto, Andrea; Sokal, Alan D.

    In: Nuclear Physics B - Proceedings Supplements, Vol. 30, No. C, 1993, p. 815-818.

    Research output: Contribution to journalArticle

    Caracciolo, Sergio ; Edwards, Robert G. ; Pelissetto, Andrea ; Sokal, Alan D. / Possible failure of asymptotic freedom in two-dimensional RP2 and RP3 σ-models. In: Nuclear Physics B - Proceedings Supplements. 1993 ; Vol. 30, No. C. pp. 815-818.
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    abstract = "We have simulated the two-dimensional RP2 and RP3 σ-models, at correlation lengths up to about 220 (resp. 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the conventional asymptotic scaling scenario at all correlation lengths less than about 109 (resp. 105). Moreover, they are consistent with a critical point at β ≈ 5.70 (resp. 6.96), only 2{\%} (resp. 5{\%}) beyond the largest β at which we ran. Preliminary studies of a mixed SN-1 RPN-1 model (i.e. isovector + isotensor action) show a similar freedom behavior when βT → ∞ with βV fixed {less-than or approximate} 0.6, while they are consistent with conventional asymptotic freedom along the lines βT βV fixed {less-than or approximate} 2. Taken as a whole, the data cast doubt on (though they do not completely exclude) the idea that RPN-1 and SN-1 σ-models lie in the same universality class.",
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    N2 - We have simulated the two-dimensional RP2 and RP3 σ-models, at correlation lengths up to about 220 (resp. 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the conventional asymptotic scaling scenario at all correlation lengths less than about 109 (resp. 105). Moreover, they are consistent with a critical point at β ≈ 5.70 (resp. 6.96), only 2% (resp. 5%) beyond the largest β at which we ran. Preliminary studies of a mixed SN-1 RPN-1 model (i.e. isovector + isotensor action) show a similar freedom behavior when βT → ∞ with βV fixed {less-than or approximate} 0.6, while they are consistent with conventional asymptotic freedom along the lines βT βV fixed {less-than or approximate} 2. Taken as a whole, the data cast doubt on (though they do not completely exclude) the idea that RPN-1 and SN-1 σ-models lie in the same universality class.

    AB - We have simulated the two-dimensional RP2 and RP3 σ-models, at correlation lengths up to about 220 (resp. 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the conventional asymptotic scaling scenario at all correlation lengths less than about 109 (resp. 105). Moreover, they are consistent with a critical point at β ≈ 5.70 (resp. 6.96), only 2% (resp. 5%) beyond the largest β at which we ran. Preliminary studies of a mixed SN-1 RPN-1 model (i.e. isovector + isotensor action) show a similar freedom behavior when βT → ∞ with βV fixed {less-than or approximate} 0.6, while they are consistent with conventional asymptotic freedom along the lines βT βV fixed {less-than or approximate} 2. Taken as a whole, the data cast doubt on (though they do not completely exclude) the idea that RPN-1 and SN-1 σ-models lie in the same universality class.

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