### Abstract

The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using the density matrix renormalization group method and coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The question of the bulk exponents (ν and γ) is addressed, and the results found are at variance with previously conjectured exact values.

Original language | English |
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Article number | 505003 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 45 |

Issue number | 50 |

Early online date | 29 Nov 2012 |

DOIs | |

Publication status | Published - 21 Dec 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

**Surface critical behaviour of the vertex-interacting self-avoiding walk on the square lattice.** / Foster, D. P.; Pinettes, C.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 45, no. 50, 505003. https://doi.org/10.1088/1751-8113/45/50/505003

}

TY - JOUR

T1 - Surface critical behaviour of the vertex-interacting self-avoiding walk on the square lattice

AU - Foster, D. P.

AU - Pinettes, C.

PY - 2012/12/21

Y1 - 2012/12/21

N2 - The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using the density matrix renormalization group method and coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The question of the bulk exponents (ν and γ) is addressed, and the results found are at variance with previously conjectured exact values.

AB - The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using the density matrix renormalization group method and coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The question of the bulk exponents (ν and γ) is addressed, and the results found are at variance with previously conjectured exact values.

U2 - 10.1088/1751-8113/45/50/505003

DO - 10.1088/1751-8113/45/50/505003

M3 - Article

VL - 45

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 50

M1 - 505003

ER -