Upper bounds for the connective constant of weighted self-avoiding walks

2025/08/04 by He, Qidong
#FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2508.01993

Abstract

Building on a work by Alm, we consider a model of weighted self-avoiding walks on a lattice and develop a method for computing upper bounds on the corresponding weighted connective constant, which we implement in a publicly available software package. The upper bounds are obtained as the dominant eigenvalues of certain matrices and provide detailed information about the convergence of the model's multivariate generating function. We discuss potential applications of our results to developing Peierls-type estimates for anisotropic contour models in statistical physics, generalizing a technique recently introduced by Fahrbach--Randall.

Citations

• Potential-weighted connective constants and uniqueness of Gibbs measures
• Weighted self-avoiding walks
• Crystalline ordering and large fugacity expansion for hard core lattice\n particles
• Scaling limit of a self-avoiding walk interacting with spatial random permutations
• A new transfer-matrix algorithm for exact enumerations: self-avoiding walks on the square lattice
• Haruspicy 2: The anisotropic generating function of self-avoiding polygons not D-finite
• A pattern theorem for lattice clusters

Related

• New upper bound for the connective constant for square-lattice self-avoiding walks
• Weighted self-avoiding walks
• Lectures on Self-Avoiding Walks
• The Hammersley-Welsh bound for self-avoiding walk revisited
• Self-avoiding Walks of Lattice Strips