TY - JOUR
T1 - Possible failure of asymptotic freedom in two-dimensional RP2 and RP3 σ-models
AU - Caracciolo, Sergio
AU - Edwards, Robert G.
AU - Pelissetto, Andrea
AU - Sokal, Alan D.
N1 - Funding Information:
The authors' research was supported in part by U.S. National Science Foundation grants DMS-8911273 and DMS-9200719, U.S. Department of Energy contract DE-FG02-90ER40581 and DE-FC05-85ER250000, NATO Collaborative Research Grant CRG 910251.
PY - 1993/3
Y1 - 1993/3
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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U2 - 10.1016/0920-5632(93)90332-Z
DO - 10.1016/0920-5632(93)90332-Z
M3 - Article
AN - SCOPUS:4243491472
SN - 2405-6014
VL - 30
SP - 815
EP - 818
JO - Nuclear and Particle Physics Proceedings
JF - Nuclear and Particle Physics Proceedings
IS - C
ER -