Connective constant of the self-avoiding walk on the triangular lattice

1986 ◽  
Vol 19 (13) ◽  
pp. 2591-2598 ◽  
Author(s):  
A J Guttmann ◽  
T R Osborn ◽  
A D Sokal
Keyword(s):  
Triangular Lattice ◽  
The Self ◽  
Connective Constant ◽  
Self Avoiding Walk

The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions

1995 ◽  
Vol 4 (3) ◽  
pp. 197-215 ◽  
Author(s):  
Takashi Hara ◽  
Gordon Slade
Keyword(s):  
Critical Point ◽  
Error Bound ◽  
The Self ◽  
Nearest Neighbour ◽  
High Dimensions ◽  
Lace Expansion ◽  
Connective Constant ◽  
Rigorous Error ◽  
Self Avoiding Walk ◽  
Self Avoiding Walks

We prove the existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on ℤd. For the critical point, defined as the reciprocal of the connective constant, the coefficients of the expansion are computed through orderd−6, with a rigorous error bound of orderd−7Our method for computing terms in the expansion also applies to percolation, and for nearest-neighbour independent Bernoulli bond percolation on ℤdgives the 1/d-expansion for the critical point through orderd−3, with a rigorous error bound of orderd−4The method uses the lace expansion.

scholarly journals New lower bounds on the self-avoiding-walk connective constant

1993 ◽  
Vol 72 (3-4) ◽  
pp. 479-517 ◽  
Author(s):  
Takashi Hara ◽  
Gordon Slade ◽  
Alan D. Sokal
Keyword(s):  
Lower Bounds ◽  
The Self ◽  
Connective Constant ◽  
Self Avoiding Walk

scholarly journals Erratum: New lower bounds on the self-avoiding-walk connective constant

1995 ◽  
Vol 78 (3-4) ◽  
pp. 1187-1188 ◽  
Author(s):  
Takashi Hara ◽  
Gordon Slade ◽  
Alan D. Sokal
Keyword(s):  
Lower Bounds ◽  
The Self ◽  
Connective Constant ◽  
Self Avoiding Walk

scholarly journals Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 153
Author(s):  
Damien Foster ◽  
Ralph Kenna ◽  
Claire Pinettes
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Critical Behavior ◽  
Finite Size ◽  
The Self ◽  
Partition Function Zeros ◽  
Adsorption Transition ◽  
Function Zeros ◽  
Complex Zeros ◽  
Self Avoiding Walk

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.

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