No-free-ends method for lattice animals and vertex models with arbitrary number of states

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5 Citations (Scopus)

Abstract

A new no-free-ends method for generating power series expansions for vertex models with arbitrary number of states is described. It is based on first-order differential equations providing a recurrent relation connecting the free-ends part of the series expansion in the (n + 1)th order with the nth and (n - 1)th order of the complete expansion. The number of necessary no-free-ends graphs can be further reduced for symmetric systems by eliminating the nodes which have two neighbors and their incident bonds are in different states.

Original languageEnglish (US)
Pages (from-to)529-539
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
Volume202
Issue number3-4
DOIs
StatePublished - Jan 15 1994
Externally publishedYes

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Lattice Animals
Animal Model
Vertex Model
Lattice Model
series expansion
animals
apexes
Power Series Expansion
power series
Arbitrary
First order differential equation
Series Expansion
differential equations
expansion
Necessary
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "A new no-free-ends method for generating power series expansions for vertex models with arbitrary number of states is described. It is based on first-order differential equations providing a recurrent relation connecting the free-ends part of the series expansion in the (n + 1)th order with the nth and (n - 1)th order of the complete expansion. The number of necessary no-free-ends graphs can be further reduced for symmetric systems by eliminating the nodes which have two neighbors and their incident bonds are in different states.",
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