Surface critical exponents of self-avoiding walks on a square lattice with an adsorbing linear boundary: A computer simulation study

Journal Article · Wed Sep 01 00:00:00 EDT 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.48.1960· OSTI ID:6252437

Meirovitch, H ^[1]; Chang, I ^[2]

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1. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052 (United States)
2. Research Center for Dielectric and Advanced Matter Physics and Department of Physics, College of Natural Sciences, Pusan National University, Pusan (Korea, Republic of)

Using the scanning simulation method, we study a model of a single self-avoiding walk (SAW) terminally attached to an adsorbing impenetrable linear boundary on a square lattice; an interaction energy [var epsilon] ([var epsilon][lt]0) is defined between the surface'' and a step (bond) that lies on the surface. SAW's of up to [ital N]=260 steps are studied from samples generated with different values of the scanning parameter, [ital b]=3 and 5. In most cases the different samples lead to the same results, which suggests that they are statistically reliable. At the ordinary point (infinite temperature [ital T]) our result for the growth parameter, [mu]=2.638 16[plus minus]0.000 02, is equal, within the error bars, to the best known estimate of Enting and Guttmann [J. Phys. A 18, 1007 (1985)]. Also, our value [gamma][sub 1]=0.9551[plus minus]0.0003 agrees very well with Cardy's value [gamma][sub 1]=61/64=0.953 . . . , obtained from conformal invariance [Nucl. Phys. B 240, 514 (1984)]. At the special point, we obtain independently the estimates [gamma][sub 1]=1.478[plus minus]0.020 and [gamma][sub 11]=0.860[plus minus]0.026 and, therefore, also two independent estimates for [mu] that are found to be equal and very close to the Enting-Guttmann value. These results for [gamma][sub 1] and [gamma][sub 11] satisfy the Barber scaling relation. However, our adsorption critical temperature [minus][var epsilon]/[ital k][sub [ital B]T][sup *]=[ital K][sup *]=0.722[plus minus]0.004 is larger than estimates previously obtained by the transfer-matrix method. Correspondingly, our result for the crossover exponent [phi]=0.562[plus minus]0.020 is significantly larger than a theoretical value of Burkhardt, Eisenriegler, and Guim [Nucl. Phys. B 316, 559 (1989)], [phi]=1/2.

• DOE Contract Number: FC05-85ER25000
• OSTI ID: 6252437
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 48:3; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ADSORPTION
SURFACES
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
CONFORMAL INVARIANCE
FREE ENERGY
MONOMERS
POLYMERS
PROTEINS
ENERGY
INVARIANCE PRINCIPLES
ORGANIC COMPOUNDS
PHYSICAL PROPERTIES
SIMULATION
SORPTION
THERMODYNAMIC PROPERTIES
360606* - Other Materials- Physical Properties- (1992-)
661300 - Other Aspects of Physical Science- (1992-)
665000 - Physics of Condensed Matter- (1992-)