TY - JOUR
T1 - Correction-to-scaling exponents for two-dimensional self-avoiding walks
AU - Caracciolo, Sergio
AU - Guttmann, Anthony J.
AU - Jensen, Iwan
AU - Pelissetto, Andrea
AU - Rogers, Andrew N.
AU - Sokal, Alan D.
N1 - Funding Information:
This research was supported in part by the Consiglio Nazionale delle Ricerche (S.C. and A.P.), the Australian Research Council (A.J.G. and I.J.), the U.S. National Science Foundation grants DMS–8911273, DMS– 9200719, PHY–9520978, PHY–9900769, PHY–0099393 and PHY–0424082 (A.D.S.), the U.S. Department of Energy contract DE-FG02-90ER40581 (A.D.S.), the NATO Collaborative Research grant CRG 910251 (S.C. and A.D.S.), and a grant from the New York University Research Challenge Fund (A.D.S.). Acknowledgment is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research under grants 21091–AC7 and 25553– AC7B–C. A.N.R. and I.J. are pleased to acknowledge computational facilities provided by both VPAC and APAC.
PY - 2005/9
Y1 - 2005/9
N2 - We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ1=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.
AB - We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ1=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.
KW - Conformal invariance
KW - Corrections to scaling
KW - Critical exponents
KW - Exact enumeration
KW - Monte Carlo
KW - Pivot algorithm
KW - Polymer
KW - Self-avoiding walk
KW - Series expansion
UR - http://www.scopus.com/inward/record.url?scp=27844546229&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=27844546229&partnerID=8YFLogxK
U2 - 10.1007/s10955-005-7004-3
DO - 10.1007/s10955-005-7004-3
M3 - Article
AN - SCOPUS:27844546229
SN - 0022-4715
VL - 120
SP - 1037
EP - 1100
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5-6
ER -