Bethe ansatz solution of the square-triangle random tiling model

Journal Article · Mon Apr 05 04:00:00 EDT 1993 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.70.2094· OSTI ID:6943341

Widom, M ^[1]

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1. Department of Physics and Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853 (United States) Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 (United States)

Random tiling models cover the plane with a set of rigid tiles without gaps between tiles and without overlap. This paper considers tilings of the plane by squares and equilateral triangles which display twelvefold rotational symmetry and quasi-long-range quasiperiodic translational order. Tiling configurations may be described as networks of interacting domain walls, for which the Bethe ansatz provides the exact (formal) partition function. Numerical evaluation yields the entropy and phason elastic constants with high accuracy.

• DOE Contract Number: FG02-89ER45405
• OSTI ID: 6943341
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 70:14; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONFIGURATION
DOMAIN STRUCTURE
ENTROPY
MECHANICS
PHYSICAL PROPERTIES
RANDOMNESS
RECTANGULAR CONFIGURATION
SQUARE CONFIGURATION
STATISTICAL MECHANICS
THERMODYNAMIC PROPERTIES
THERMODYNAMICS
TRIANGULAR CONFIGURATION