Special transitions in an O(n) loop model with an Ising-like constraint

Zhe Fu, Wenan Guo, and Henk W. J. Blöte
Phys. Rev. E 93, 042108 – Published 8 April 2016

Abstract

We investigate the O(n) nonintersecting loop model on the square lattice under the constraint that the loops consist of 90-deg bends only. The model is governed by the loop weight n, a weight x for each vertex of the lattice visited once by a loop, and a weight z for each vertex visited twice by a loop. We explore the (x,z) phase diagram for some values of n. For 0<n<1, the diagram has the same topology as the generic O(n) phase diagram with n<2, with a first-order line when z starts to dominate and an O(n)-like transition when x starts to dominate. Both lines meet in an exactly solved higher critical point. For n>1, the O(n)-like transition line appears to be absent. Thus, for z=0, the (n,x) phase diagram displays a line of phase transitions for n1. The line ends at n=1 in an infinite-order transition. We determine the conformal anomaly and the critical exponents along this line. These results agree accurately with a recent proposal for the universal classification of this type of model, at least in most of the range 1n1. We also determine the exponent describing crossover to the generic O(n) universality class, by introducing topological defects associated with the introduction of “straight” vertices violating the 90-deg-bend rule. These results are obtained by means of transfer-matrix calculations and finite-size scaling.

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  • Received 7 February 2016

DOI:https://doi.org/10.1103/PhysRevE.93.042108

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Techniques
Statistical Physics & Thermodynamics

Authors & Affiliations

Zhe Fu1, Wenan Guo2,*, and Henk W. J. Blöte2,3,†

  • 1College of Physics and Electronic Engineering, Xinxiang University, Xinxiang 453003, People's Republic of China
  • 2Physics Department, Beijing Normal University, Beijing 100875, People's Republic of China
  • 3Instituut Lorentz, Leiden University, Post Office Box 9506, 2300 RA Leiden, The Netherlands

  • *Corresponding author: waguo@bnu.edu.cn
  • henk@lorentz.leidenuniv.nl

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Issue

Vol. 93, Iss. 4 — April 2016

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