Tricritical trails on a square lattice with impenetrable linear boundary: Computer simulation and analytic bounds

Journal Article · Thu Feb 15 04:00:00 EST 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.41.1808· OSTI ID:7165143

Chang, I S ^[1]; Meirovitch, H ^[2]; Shapir, Y ^[1]

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1. Department of Physics and Astronomy, University of Rochester, Rochester, New York, 14627-0011 (USA)
2. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052 (USA)

Using the scanning simulation method we study self-attracting trails (with energy {var epsilon} per intersection) terminally attached to an impenetrable linear boundary on a square lattice, at their tricritical collapse transition. We obtain (with 95% confidence limits) that the partition function exponents are {gamma}{sub 1{ital t}}=0.634{plus minus}0.025 (for trails with one end attached to the boundary) and {gamma}{sub 11{ital t}}={minus}0.44{plus minus}0.02 (both ends are attached). These results differ significantly from the exact values (8/7{congruent}1.143 and 4/7{congruent}0.571), respectively, derived by Duplantier and Saleur (DS) (Phys. Rev. Lett. 59, 539 (1987)) for self-avoiding walks (SAW's) on a dilute hexagonal lattice at the {ital FTHETA}{prime} point. Our values are within the error bars of the numerical estimates of Seno and Stella for SAW's on the same lattice at the {ital FTHETA} point. The crossover exponent is calculated in several ways and the various results approximately converge to {phi}{sub {ital t}}{congruent}0.71 if corrections to scaling are taken into account. This value is significantly larger than the DS exact value for the {ital FTHETA}{prime} point {phi}=3/7{congruent}0.43; it is also larger than recent numerical estimates of {phi}{sub {ital t}} for SAW's at the {ital FTHETA} point. These results suggest that tricritical trails are in a different universality class than SAW's in both the {ital FTHETA} and the {ital FTHETA}{prime} point. The results for the shape exponent {nu}{sub {ital t}} are consistent with the DS value 4/7{congruent}0.571.

• OSTI ID: 7165143
• Journal Information: Physical Review, A (General Physics); (USA), Journal Name: Physical Review, A (General Physics); (USA) Vol. 41:4; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
CRITICAL TEMPERATURE
FILMS
INTERMOLECULAR FORCES
PHYSICAL PROPERTIES
POLYMERS
SIMULATION
SOLVENTS
THERMODYNAMIC PROPERTIES
TRAJECTORIES
TRANSITION TEMPERATURE