Critical phenomena in semi-infinite systems

1982/01/01 by J. M. Hammersley · 1 citation
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Quantum chaos and dynamical systems

paper · doi:10.2307/3213572

Abstract

This paper discusses the asymptotic behaviour, and in particular the critical singularities, of the generating functions for Pólya walks with a given fraction of visits to a hyperplane when the walk is or is not constrained to be on one side of that hyperplane. The three-dimensional case has applications in physics and chemistry.

Cited by

• Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

Related

• A shape theorem for the scaling limit of the IPDSAW at criticality
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
• Sinaĭ excursions: An analogue of Sparre Andersen's formula for the area process of a random walk
• Polya's random walk theorem
• The near-critical two-point function and the torus plateau for weakly self-avoiding walk in high dimensions