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Yaroslav Bulatov
Yaroslav Bulatov
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Suppose we have an undirected graph with integer valued nodes where node $i$ is connected to$0<|i-j|\le 2$ implies nodes $i+1$$i$ and $i+2$$j$ are connected. Let $c_n$ be the number of self-avoiding walks on this graph of length $n$ starting at origin. Define the connective constant as

$$\mu = \lim_{n\to \infty} c_n^{\frac{1}{n}}$$

What is known about $\mu$? This quantity seems to be related to the transition temperature of an Ising model on such graph, has such model been studied?

Suppose we have an undirected graph with integer valued nodes where node $i$ is connected to nodes $i+1$ and $i+2$. Let $c_n$ be the number of self-avoiding walks on this graph of length $n$ starting at origin. Define the connective constant as

$$\mu = \lim_{n\to \infty} c_n^{\frac{1}{n}}$$

What is known about $\mu$? This quantity seems to be related to the transition temperature of an Ising model on such graph, has such model been studied?

Suppose we have an undirected graph with integer valued nodes where $0<|i-j|\le 2$ implies nodes $i$ and $j$ are connected. Let $c_n$ be the number of self-avoiding walks on this graph of length $n$ starting at origin. Define the connective constant as

$$\mu = \lim_{n\to \infty} c_n^{\frac{1}{n}}$$

What is known about $\mu$? This quantity seems to be related to the transition temperature of an Ising model on such graph, has such model been studied?

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Yaroslav Bulatov
Yaroslav Bulatov
  • 2.4k
  • 21
  • 40

Connective constant for self-avoiding walks on a skip-chain

Suppose we have an undirected graph with integer valued nodes where node $i$ is connected to nodes $i+1$ and $i+2$. Let $c_n$ be the number of self-avoiding walks on this graph of length $n$ starting at origin. Define the connective constant as

$$\mu = \lim_{n\to \infty} c_n^{\frac{1}{n}}$$

What is known about $\mu$? This quantity seems to be related to the transition temperature of an Ising model on such graph, has such model been studied?