Abstract
We investigate the 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 , a weight for each vertex of the lattice visited once by a loop, and a weight for each vertex visited twice by a loop. We explore the phase diagram for some values of . For , the diagram has the same topology as the generic phase diagram with , with a first-order line when starts to dominate and an -like transition when starts to dominate. Both lines meet in an exactly solved higher critical point. For , the -like transition line appears to be absent. Thus, for , the phase diagram displays a line of phase transitions for . The line ends at 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 . We also determine the exponent describing crossover to the generic 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.
4 More- Received 7 February 2016
DOI:https://doi.org/10.1103/PhysRevE.93.042108
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