Morin-Duchesne, Alexi and Saint-Aubin, Yvan (2013) Jordan cells of periodic loop models. Journal of Physics A: Mathematical and Theoretical, 4649: 494013.1-494013.47. doi:10.1088/1751-8113/46/49/494013
Jordan cells in transfer matrices of finite lattice models are a signature of the logarithmic character of the conformal field theories that appear in their thermodynamical limit. The transfer matrix of periodic loop models, T N, is an element of the periodic Temperley-Lieb algebra , where N is the number of sites on a section of the cylinder, and β = -q - q-1 = 2cos λ and the weights of contractible and non-contractible loops. The thermodynamic limit of TN is believed to describe a conformal field theory of central charge c = 1 - 6λ 2/(π(λ - π)). The abstract element TN acts naturally on (a sum of) spaces , similar to those upon which the standard modules of the (classical) Temperley-Lieb algebra act. These spaces known as sectors are labeled by the numbers of defects d and depend on a twist parameter v that keeps track of the winding of defects around the cylinder. Criteria are given for non-trivial Jordan cells of TN both between sectors with distinct defect numbers and within a given sector.