### 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 language | English (US) |
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Pages (from-to) | 529-539 |

Number of pages | 11 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 202 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 15 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**No-free-ends method for lattice animals and vertex models with arbitrary number of states.** / Kolesik, Miroslav.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - No-free-ends method for lattice animals and vertex models with arbitrary number of states

AU - Kolesik, Miroslav

PY - 1994/1/15

Y1 - 1994/1/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=23544480508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23544480508&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(94)90477-4

DO - 10.1016/0378-4371(94)90477-4

M3 - Article

VL - 202

SP - 529

EP - 539

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3-4

ER -