Finite-size corrections for inclined interfaces in two dimensions: Exact results for Ising and solid-on-solid models

1988 ◽  
Vol 53 (5-6) ◽  
pp. 1041-1059 ◽  
Author(s):  
N. M. Svrakić ◽  
V. Privman ◽  
D. B. Abraham
Keyword(s):  
Finite Size ◽  
Two Dimensions ◽  
Exact Results ◽  
Solid Models ◽  
Finite Size Corrections

scholarly journals Finite-size corrections for universal boundary entropy in bond percolation

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Jan de Gier ◽  
Jesper Jacobsen ◽  
Anita Ponsaing
Keyword(s):  
Field Theory ◽  
Arbitrary Order ◽  
Finite Size ◽  
Square Lattice ◽  
Bond Percolation ◽  
Exact Results ◽  
Conformal Field ◽  
Logarithmic Corrections ◽  
Special Value ◽  
Finite Size Corrections

We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size LL. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finite-size corrections to arbitrary order. For the strip we provide exact expressions that have been verified using high-precision numerical analysis. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight.

Crystal to Glass Transition and Melting in Two Dimensions

1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard
Keyword(s):  
Glass Transition ◽  
Intermediate Phase ◽  
Orientational Order ◽  
Finite Size ◽  
Two Dimensions ◽  
Size Difference ◽  
Two Dimensional ◽  
Atomic Size ◽  
Bond Orientational Order ◽  
Dynamics Simulations

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.

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