Abstract
Abstract
Fekete’s lemma shows the existence of limits in subadditive sequences. This lemma, and generalisations of it, also have been used to prove the existence of thermodynamic limits in statistical mechanics. In this paper it is shown that the two variable supermultiplicative relation
p
n
1
(
m
1
)
p
n
2
(
m
2
)
⩽
p
n
1
+
n
2
(
m
1
+
m
2
)
together with mild assumptions, imply the existence of the limit
log
P
#
(
ϵ
)
=
lim
n
→
∞
1
n
log
p
n
(
⌊
ϵ
n
⌋
)
.
This is a generalisation of Fekete’s lemma. The existence of
log
P
#
(
ϵ
)
is proven for models of adsorbing walks and polygons, and for pulled polygons. In addition, numerical data are presented estimating the general shape of
log
P
#
(
ϵ
)
of models of square lattice self-avoiding walks and polygons.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
1 articles.
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